algebra.lie.universal_enveloping
⟷
Mathlib.Algebra.Lie.UniversalEnveloping
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -91,7 +91,7 @@ def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
map_lie' := fun x y =>
by
suffices mk_alg_hom R L (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) = mk_alg_hom R L (ιₜ x * ιₜ y) by
- rw [AlgHom.map_mul] at this ; simp [LieRing.of_associative_ring_bracket, ← this]
+ rw [AlgHom.map_mul] at this; simp [LieRing.of_associative_ring_bracket, ← this]
exact RingQuot.mkAlgHom_rel _ (rel.lie_compat x y) }
#align universal_enveloping_algebra.ι UniversalEnvelopingAlgebra.ι
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
-import Mathbin.Algebra.Lie.OfAssociative
-import Mathbin.Algebra.RingQuot
-import Mathbin.LinearAlgebra.TensorAlgebra.Basic
+import Algebra.Lie.OfAssociative
+import Algebra.RingQuot
+import LinearAlgebra.TensorAlgebra.Basic
#align_import algebra.lie.universal_enveloping from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.universal_enveloping
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Lie.OfAssociative
import Mathbin.Algebra.RingQuot
import Mathbin.LinearAlgebra.TensorAlgebra.Basic
+#align_import algebra.lie.universal_enveloping from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
/-!
# Universal enveloping algebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -115,14 +115,14 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
invFun F := (F : UniversalEnvelopingAlgebra R L →ₗ⁅R⁆ A).comp (ι R)
left_inv f := by ext;
simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_to_lieHom,
+ LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_toLieHom,
LieHom.coe_mk, Function.comp_apply, AlgHom.toLinearMap_apply,
RingQuot.liftAlgHom_mkAlgHom_apply]
right_inv F := by ext;
simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_to_lieHom, LieHom.coe_mk]
+ RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_toLieHom, LieHom.coe_mk]
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -48,7 +48,6 @@ variable (R : Type u₁) (L : Type u₂)
variable [CommRing R] [LieRing L] [LieAlgebra R L]
--- mathport name: exprιₜ
local notation "ιₜ" => TensorAlgebra.ι R
namespace UniversalEnvelopingAlgebra
@@ -78,14 +77,17 @@ deriving Inhabited, Ring,
namespace UniversalEnvelopingAlgebra
+#print UniversalEnvelopingAlgebra.mkAlgHom /-
/-- The quotient map from the tensor algebra to the universal enveloping algebra as a morphism of
associative algebras. -/
def mkAlgHom : TensorAlgebra R L →ₐ[R] UniversalEnvelopingAlgebra R L :=
RingQuot.mkAlgHom R (Rel R L)
#align universal_enveloping_algebra.mk_alg_hom UniversalEnvelopingAlgebra.mkAlgHom
+-/
variable {L}
+#print UniversalEnvelopingAlgebra.ι /-
/-- The natural Lie algebra morphism from a Lie algebra to its universal enveloping algebra. -/
def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
{ (mkAlgHom R L).toLinearMap.comp ιₜ with
@@ -95,9 +97,11 @@ def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
rw [AlgHom.map_mul] at this ; simp [LieRing.of_associative_ring_bracket, ← this]
exact RingQuot.mkAlgHom_rel _ (rel.lie_compat x y) }
#align universal_enveloping_algebra.ι UniversalEnvelopingAlgebra.ι
+-/
variable {A : Type u₃} [Ring A] [Algebra R A] (f : L →ₗ⁅R⁆ A)
+#print UniversalEnvelopingAlgebra.lift /-
/-- The universal property of the universal enveloping algebra: Lie algebra morphisms into
associative algebras lift to associative algebra morphisms from the universal enveloping algebra. -/
def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
@@ -120,29 +124,39 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_to_lieHom, LieHom.coe_mk]
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
+-/
+#print UniversalEnvelopingAlgebra.lift_symm_apply /-
@[simp]
theorem lift_symm_apply (F : UniversalEnvelopingAlgebra R L →ₐ[R] A) :
(lift R).symm F = (F : UniversalEnvelopingAlgebra R L →ₗ⁅R⁆ A).comp (ι R) :=
rfl
#align universal_enveloping_algebra.lift_symm_apply UniversalEnvelopingAlgebra.lift_symm_apply
+-/
+#print UniversalEnvelopingAlgebra.ι_comp_lift /-
@[simp]
theorem ι_comp_lift : lift R f ∘ ι R = f :=
funext <| LieHom.ext_iff.mp <| (lift R).symm_apply_apply f
#align universal_enveloping_algebra.ι_comp_lift UniversalEnvelopingAlgebra.ι_comp_lift
+-/
+#print UniversalEnvelopingAlgebra.lift_ι_apply /-
@[simp]
theorem lift_ι_apply (x : L) : lift R f (ι R x) = f x := by
rw [← Function.comp_apply (lift R f) (ι R) x, ι_comp_lift]
#align universal_enveloping_algebra.lift_ι_apply UniversalEnvelopingAlgebra.lift_ι_apply
+-/
+#print UniversalEnvelopingAlgebra.lift_unique /-
theorem lift_unique (g : UniversalEnvelopingAlgebra R L →ₐ[R] A) : g ∘ ι R = f ↔ g = lift R f :=
by
refine' Iff.trans _ (lift R).symm_apply_eq
constructor <;> · intro h; ext; simp [← h]
#align universal_enveloping_algebra.lift_unique UniversalEnvelopingAlgebra.lift_unique
+-/
+#print UniversalEnvelopingAlgebra.hom_ext /-
/-- See note [partially-applied ext lemmas]. -/
@[ext]
theorem hom_ext {g₁ g₂ : UniversalEnvelopingAlgebra R L →ₐ[R] A}
@@ -153,6 +167,7 @@ theorem hom_ext {g₁ g₂ : UniversalEnvelopingAlgebra R L →ₐ[R] A}
have h' : (lift R).symm g₁ = (lift R).symm g₂ := by ext; simp [h]
(lift R).symm.Injective h'
#align universal_enveloping_algebra.hom_ext UniversalEnvelopingAlgebra.hom_ext
+-/
end UniversalEnvelopingAlgebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
! This file was ported from Lean 3 source module algebra.lie.universal_enveloping
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.TensorAlgebra.Basic
/-!
# Universal enveloping algebra
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given a commutative ring `R` and a Lie algebra `L` over `R`, we construct the universal
enveloping algebra of `L`, together with its universal property.
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -50,6 +50,7 @@ local notation "ιₜ" => TensorAlgebra.ι R
namespace UniversalEnvelopingAlgebra
+#print UniversalEnvelopingAlgebra.Rel /-
/-- The quotient by the ideal generated by this relation is the universal enveloping algebra.
Note that we have avoided using the more natural expression:
@@ -58,16 +59,19 @@ so that our construction needs only the semiring structure of the tensor algebra
inductive Rel : TensorAlgebra R L → TensorAlgebra R L → Prop
| lie_compat (x y : L) : Rel (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) (ιₜ x * ιₜ y)
#align universal_enveloping_algebra.rel UniversalEnvelopingAlgebra.Rel
+-/
end UniversalEnvelopingAlgebra
/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R -/
+#print UniversalEnvelopingAlgebra /-
/-- The universal enveloping algebra of a Lie algebra. -/
def UniversalEnvelopingAlgebra :=
RingQuot (UniversalEnvelopingAlgebra.Rel R L)
deriving Inhabited, Ring,
«./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R»
#align universal_enveloping_algebra UniversalEnvelopingAlgebra
+-/
namespace UniversalEnvelopingAlgebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -61,12 +61,12 @@ inductive Rel : TensorAlgebra R L → TensorAlgebra R L → Prop
end UniversalEnvelopingAlgebra
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R -/
/-- The universal enveloping algebra of a Lie algebra. -/
def UniversalEnvelopingAlgebra :=
RingQuot (UniversalEnvelopingAlgebra.Rel R L)
deriving Inhabited, Ring,
- «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R»
+ «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R»
#align universal_enveloping_algebra UniversalEnvelopingAlgebra
namespace UniversalEnvelopingAlgebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -64,7 +64,8 @@ end UniversalEnvelopingAlgebra
/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R -/
/-- The universal enveloping algebra of a Lie algebra. -/
def UniversalEnvelopingAlgebra :=
- RingQuot (UniversalEnvelopingAlgebra.Rel R L)deriving Inhabited, Ring,
+ RingQuot (UniversalEnvelopingAlgebra.Rel R L)
+deriving Inhabited, Ring,
«./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R»
#align universal_enveloping_algebra UniversalEnvelopingAlgebra
@@ -84,7 +85,7 @@ def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
map_lie' := fun x y =>
by
suffices mk_alg_hom R L (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) = mk_alg_hom R L (ιₜ x * ιₜ y) by
- rw [AlgHom.map_mul] at this; simp [LieRing.of_associative_ring_bracket, ← this]
+ rw [AlgHom.map_mul] at this ; simp [LieRing.of_associative_ring_bracket, ← this]
exact RingQuot.mkAlgHom_rel _ (rel.lie_compat x y) }
#align universal_enveloping_algebra.ι UniversalEnvelopingAlgebra.ι
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -83,10 +83,8 @@ def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
{ (mkAlgHom R L).toLinearMap.comp ιₜ with
map_lie' := fun x y =>
by
- suffices mk_alg_hom R L (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) = mk_alg_hom R L (ιₜ x * ιₜ y)
- by
- rw [AlgHom.map_mul] at this
- simp [LieRing.of_associative_ring_bracket, ← this]
+ suffices mk_alg_hom R L (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) = mk_alg_hom R L (ιₜ x * ιₜ y) by
+ rw [AlgHom.map_mul] at this; simp [LieRing.of_associative_ring_bracket, ← this]
exact RingQuot.mkAlgHom_rel _ (rel.lie_compat x y) }
#align universal_enveloping_algebra.ι UniversalEnvelopingAlgebra.ι
@@ -103,14 +101,12 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
simp only [LieRing.of_associative_ring_bracket, map_add, TensorAlgebra.lift_ι_apply,
LieHom.coe_toLinearMap, LieHom.map_lie, map_mul, sub_add_cancel]⟩
invFun F := (F : UniversalEnvelopingAlgebra R L →ₗ⁅R⁆ A).comp (ι R)
- left_inv f := by
- ext
+ left_inv f := by ext;
simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_to_lieHom,
LieHom.coe_mk, Function.comp_apply, AlgHom.toLinearMap_apply,
RingQuot.liftAlgHom_mkAlgHom_apply]
- right_inv F := by
- ext
+ right_inv F := by ext;
simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
@@ -136,10 +132,7 @@ theorem lift_ι_apply (x : L) : lift R f (ι R x) = f x := by
theorem lift_unique (g : UniversalEnvelopingAlgebra R L →ₐ[R] A) : g ∘ ι R = f ↔ g = lift R f :=
by
refine' Iff.trans _ (lift R).symm_apply_eq
- constructor <;>
- · intro h
- ext
- simp [← h]
+ constructor <;> · intro h; ext; simp [← h]
#align universal_enveloping_algebra.lift_unique UniversalEnvelopingAlgebra.lift_unique
/-- See note [partially-applied ext lemmas]. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -101,17 +101,17 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
⟨TensorAlgebra.lift R (f : L →ₗ[R] A), by
intro a b h; induction' h with x y
simp only [LieRing.of_associative_ring_bracket, map_add, TensorAlgebra.lift_ι_apply,
- LieHom.coe_to_linearMap, LieHom.map_lie, map_mul, sub_add_cancel]⟩
+ LieHom.coe_toLinearMap, LieHom.map_lie, map_mul, sub_add_cancel]⟩
invFun F := (F : UniversalEnvelopingAlgebra R L →ₗ⁅R⁆ A).comp (ι R)
left_inv f := by
ext
- simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_to_linearMap,
+ simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_to_lieHom,
LieHom.coe_mk, Function.comp_apply, AlgHom.toLinearMap_apply,
RingQuot.liftAlgHom_mkAlgHom_apply]
right_inv F := by
ext
- simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_to_linearMap,
+ simp only [ι, mk_alg_hom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_to_lieHom, LieHom.coe_mk]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -88,7 +88,7 @@ def mkAlgHom : TensorAlgebra R L →ₐ[R] UniversalEnvelopingAlgebra R L :=
variable {L}
/-- The natural Lie algebra morphism from a Lie algebra to its universal enveloping algebra. -/
-@[simps!] -- Porting note: added
+@[simps!] -- Porting note (#11445): added
def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
{ (mkAlgHom R L).toLinearMap.comp ιₜ with
map_lie' := fun {x y} => by
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -39,7 +39,6 @@ lie algebra, universal enveloping algebra, tensor algebra
universe u₁ u₂ u₃
variable (R : Type u₁) (L : Type u₂)
-
variable [CommRing R] [LieRing L] [LieAlgebra R L]
local notation "ιₜ" => TensorAlgebra.ι R
@@ -119,7 +119,8 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [LieHom.coe_comp, Function.comp_apply, AlgHom.coe_toLieHom,
UniversalEnvelopingAlgebra.ι_apply, mkAlgHom]
- rw [RingQuot.liftAlgHom_mkAlgHom_apply]
+ -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+ erw [RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap]
right_inv F := by
apply RingQuot.ringQuot_ext'
@@ -129,7 +130,8 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
-- AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
-- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_toLieHom, LieHom.coe_mk]
- simp [mkAlgHom]
+ -- extra `rfl` after leanprover/lean4#2644
+ simp [mkAlgHom]; rfl
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
@[simp]
@@ -119,8 +119,7 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [LieHom.coe_comp, Function.comp_apply, AlgHom.coe_toLieHom,
UniversalEnvelopingAlgebra.ι_apply, mkAlgHom]
- -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
- erw [RingQuot.liftAlgHom_mkAlgHom_apply]
+ rw [RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap]
right_inv F := by
apply RingQuot.ringQuot_ext'
@@ -130,8 +129,7 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
-- AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
-- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_toLieHom, LieHom.coe_mk]
- -- extra `rfl` after leanprover/lean4#2644
- simp [mkAlgHom]; rfl
+ simp [mkAlgHom]
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
@[simp]
@@ -119,7 +119,8 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [LieHom.coe_comp, Function.comp_apply, AlgHom.coe_toLieHom,
UniversalEnvelopingAlgebra.ι_apply, mkAlgHom]
- rw [RingQuot.liftAlgHom_mkAlgHom_apply]
+ -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+ erw [RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap]
right_inv F := by
apply RingQuot.ringQuot_ext'
@@ -129,7 +130,8 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
-- AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
-- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_toLieHom, LieHom.coe_mk]
- simp [mkAlgHom]
+ -- extra `rfl` after leanprover/lean4#2644
+ simp [mkAlgHom]; rfl
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
@[simp]
@@ -2,16 +2,13 @@
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.universal_enveloping
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.RingQuot
import Mathlib.LinearAlgebra.TensorAlgebra.Basic
+#align_import algebra.lie.universal_enveloping from "leanprover-community/mathlib"@"32b08ef840dd25ca2e47e035c5da03ce16d2dc3c"
+
/-!
# Universal enveloping algebra
@@ -45,7 +45,6 @@ variable (R : Type u₁) (L : Type u₂)
variable [CommRing R] [LieRing L] [LieAlgebra R L]
--- mathport name: exprιₜ
local notation "ιₜ" => TensorAlgebra.ι R
namespace UniversalEnvelopingAlgebra
@@ -68,7 +67,8 @@ def UniversalEnvelopingAlgebra :=
namespace UniversalEnvelopingAlgebra
--- Porting note: the next three instances were derived automatically in mathlib3.
+-- Porting note(https://github.com/leanprover-community/mathlib4/issues/5020): the next three
+-- instances were derived automatically in mathlib3.
instance instInhabited : Inhabited (UniversalEnvelopingAlgebra R L) :=
inferInstanceAs (Inhabited (RingQuot (UniversalEnvelopingAlgebra.Rel R L)))
@@ -97,7 +97,7 @@ def ι : L →ₗ⁅R⁆ UniversalEnvelopingAlgebra R L :=
{ (mkAlgHom R L).toLinearMap.comp ιₜ with
map_lie' := fun {x y} => by
suffices mkAlgHom R L (ιₜ ⁅x, y⁆ + ιₜ y * ιₜ x) = mkAlgHom R L (ιₜ x * ιₜ y) by
- rw [AlgHom.map_mul] at this ; simp [LieRing.of_associative_ring_bracket, ← this]
+ rw [AlgHom.map_mul] at this; simp [LieRing.of_associative_ring_bracket, ← this]
exact RingQuot.mkAlgHom_rel _ (Rel.lie_compat x y) }
#align universal_enveloping_algebra.ι UniversalEnvelopingAlgebra.ι
@@ -117,10 +117,10 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
ext
-- Porting note: was
-- simp only [ι, mkAlgHom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
- -- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_to_lieHom,
+ -- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_comp, AlgHom.coe_toLieHom,
-- LieHom.coe_mk, Function.comp_apply, AlgHom.toLinearMap_apply,
-- RingQuot.liftAlgHom_mkAlgHom_apply]
- simp only [LieHom.coe_comp, Function.comp_apply, AlgHom.coe_to_lieHom,
+ simp only [LieHom.coe_comp, Function.comp_apply, AlgHom.coe_toLieHom,
UniversalEnvelopingAlgebra.ι_apply, mkAlgHom]
rw [RingQuot.liftAlgHom_mkAlgHom_apply]
simp only [TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap]
@@ -131,7 +131,7 @@ def lift : (L →ₗ⁅R⁆ A) ≃ (UniversalEnvelopingAlgebra R L →ₐ[R] A)
-- simp only [ι, mkAlgHom, TensorAlgebra.lift_ι_apply, LieHom.coe_toLinearMap,
-- LinearMap.toFun_eq_coe, LinearMap.coe_comp, LieHom.coe_linearMap_comp,
-- AlgHom.comp_toLinearMap, Function.comp_apply, AlgHom.toLinearMap_apply,
- -- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_to_lieHom, LieHom.coe_mk]
+ -- RingQuot.liftAlgHom_mkAlgHom_apply, AlgHom.coe_toLieHom, LieHom.coe_mk]
simp [mkAlgHom]
#align universal_enveloping_algebra.lift UniversalEnvelopingAlgebra.lift
The unported dependencies are