Is there a standard name/notation for ...

Stream: new members

[Kevin Sullivan]

Is there a standard name/notation for the groupoid of affine coordinate space isomorphisms over an underlying (coordinate-free) affine space, S, analogous to the name general linear group, GL(V), for the automorphism group of V? Thank you, as always. With kind regards, Kevin

[Yaël Dillies]

This was previously discussed here: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/What's.20the.20name.20of.20this.20mathematical.20structure

[Kevin Sullivan]

Yaël Dillies said:

This was previously discussed here: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/What's.20the.20name.20of.20this.20mathematical.20structure

Thank you, Yaël. This is a distinct question from the one kindly answered there. That one reminded me that groupoid was the right answer. This one is asking for the standard name of a particular groupoid, namely the groupoid of affine coordinate space isomorphisms over an underlying (generally coordinate-free) affine space, S.

Love this community,
Kevin

[Kevin Buzzard]

Why not just call it the group of affine isomorphisms? I don't know any standard notation for this (but then again I don't work in the area...)

[Kevin Sullivan]

Kevin Buzzard said:

Why not just call it the group of affine isomorphisms? I don't know any standard notation for this (but then again I don't work in the area...)

Thank you Kevin. That sounds right. In which case I guess I can just make up a notation/name, e.g., AI(S). If you or anyone else has a better name for it, I'd be happy to consider swapping in suggested alternatives. Thank you, again. --Kevin