Documentation

Mathlib.Algebra.Lie.BaseChange

Extension and restriction of scalars for Lie algebras #

Lie algebras have a well-behaved theory of extension and restriction of scalars.

Main definitions #

Tags #

lie ring, lie algebra, extension of scalars, restriction of scalars, base change

@[simp]
theorem LieAlgebra.ExtendScalars.bracket_tmul (R : Type u) (A : Type w) (L : Type v) [CommRing R] [CommRing A] [Algebra R A] [LieRing L] [LieAlgebra R L] (s : A) (t : A) (x : L) (y : L) :
instance LieAlgebra.ExtendScalars.lieAlgebra (R : Type u) (A : Type w) (L : Type v) [CommRing R] [CommRing A] [Algebra R A] [LieRing L] [LieAlgebra R L] :
instance LieAlgebra.RestrictScalars.lieAlgebra (R : Type u) (A : Type w) (L : Type v) [h : LieRing L] [CommRing A] [LieAlgebra A L] [CommRing R] [Algebra R A] :