Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorjim_stasheff
   • CommentTimeJun 16th 2013
   • PermaLink
   Author: jim_stasheff
   Format: TextWhere is there written a Lie algebra analog of e.g. Koszul-Tate resolution?

   Where is there written a Lie algebra analog of e.g. Koszul-Tate resolution?
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexHi Jim, since a Koszul-Tate resolution is a homotopy (co-)fiber (of an ideal inclusion), you are maybe looking for models for homotopy fibers of maps of Lie algebras / $L_\infty$-algebras? Just recently we described an explicit such model [here](http://ncatlab.org/nlab/show/model+structure+for+L-infinity+algebras#HomotopyFiberProducts), see [theorem 3.1.13](http://arxiv.org/abs/1304.6292).

   Hi Jim,

   since a Koszul-Tate resolution is a homotopy (co-)fiber (of an ideal inclusion), you are maybe looking for models for homotopy fibers of maps of Lie algebras / $L_\infty$-algebras?

   Just recently we described an explicit such model here, see theorem 3.1.13.

3. • CommentRowNumber3.
   • CommentAuthorjim_stasheff
   • CommentTimeJun 17th 2013
   • PermaLink
   Author: jim_stasheff
   Format: TextThanks. That's just for the case of the range being abelian if I understand. Now haow about the general case. I'd also like to see it in concrete terms. Suppose L is a Lie or L_oo algebra and an A-module but not an A-Lie algebra (cf. structure functions). Let A<x,y,z,..> \to L be onto. Now repeat with A<a,b,c,...> onto the kernel of that.... anyone seen anything like that?

   Thanks. That's just for the case of the range being abelian if I understand. Now haow about the general case. I'd also like to see it
   in concrete terms. Suppose L is a Lie or L_oo algebra and an A-module
   but not an A-Lie algebra (cf. structure functions). Let A<x,y,z,..> \to L
   be onto. Now repeat with A<a,b,c,...> onto the kernel of that....
   
   anyone seen anything like that?