Talk:Lie algebra cohomology

Latest comment: 3 years ago by Wundzer in topic Examples Needed

The link to Weyl's theorem currently leads to a disambiguation page. Someone with more knowledge of the subject should correct the link to lead to a specific article.--Bill 19:59, 3 February 2006 (UTC)Reply

I am going to add some stuff to this from Kassel's quantum groups text unless someone strenuously objects. Myrkkyhammas 16:42, 17 April 2007 (UTC)Reply

Invariants

edit

I fixed a bug in the definition of the invariants module. For a Lie algebra  , the invariants of a  -module are the elements   such that   for all  . Then the action on   is trivial (as an endomorphism). For a Lie group   the invariants are the elements such that   for all   so the action on   is trivial (as an isomorphism). --Xtquique (talk) 19:20, 14 August 2014 (UTC)xtquiqueReply

Examples Needed

edit

Elementary examples of lie algebra cohomology are needed. In addition, theorems related to the de-Rham cohomology of Lie groups and their lie algebras needs to be added. — Preceding unsigned comment added by 73.181.114.81 (talk) 01:05, 29 May 2017 (UTC)Reply

agreed, I tried to develop the de Rham direction a bit Olivier Peltre (talk) 17:48, 2 April 2018 (UTC)Reply
Great work! Wundzer (talk) 21:13, 14 December 2020 (UTC)Reply

Some resources

edit

Wundzer (talk) 21:13, 14 December 2020 (UTC)Reply

Completing and elaborating the article

edit

I will try to develop the article a bit and add a few more references (Cartan, Koszul...). Also in my opinion, the definition with Ext and Tor would be more suited later on as it is a bit over-kill in this case and requires solid knowledge in category theory. Any comments and suggestions welcome! Olivier Peltre (talk) 17:48, 2 April 2018 (UTC)Reply

Missing definitions

edit

In the Cohomology in small dimensions section we see this:

The second cohomology group

 

is the space of equivalence classes of Lie algebra extensions

 

of the Lie algebra by the module  .

A bit hard to understand this because of some lacking definitions.

  1. The Lie algebra extensions article defines only extensions by a Lie algebra, not by a module.
  2. And I think, that 'module' means here a  -module, but the definition of  -module is missing from Wikipedia.
  3. According to the introduction, this is related with a concept of Lie module which is also missing from Wikipedia. — Preceding unsigned comment added by 89.135.79.17 (talk) 05:34, 7 October 2019 (UTC)Reply