# [ALGTOP-L] another request

Johannes.Huebschmann at math.univ-lille1.fr Johannes.Huebschmann at math.univ-lille1.fr
Fri Jun 11 09:05:50 EDT 2010

Dear All

Indeed, I have extended the notion of Lie-Rinehart algebra
to the differential graded setting, even to a higher homotopies version.

More details and more literature can be found in

Lie-Rinehart algebras, descent, and quantizazion,
Fields I Comm 43(2004), 295-316, math.DG/0303016

Higher homotopies and Maurer-Cartan algebras, ...
in: Festschrift in honor of Alan Weinstein,
Progress in Math. 232, math.SG/03011294

Best wishes

Johannes

> Hi Jim,
>
> the page
>
> http://ncatlab.org/nlab/show/Lie-Rinehart+pair
>
> may have what you want. A Lie-Rinehart pair is essentially an
associative
> algebra A, a Lie algebra g, A is a g-module, g is an A-module
(compatibly)
> and there is a map g --> Der(A) of Lie algebras, a map A --> End(g) of
associative algebras satisfying some 'obvious' conditions (see the link
for
> details). A Lie algebroid is the special case when A = C^\infty(X).
>
> I'm sure this could be rewritten so as to replace A by a dga, g by an
L_oo
> algebra and so on.
>
> Cheers,
>
> David
>
> On 10 June 2010 22:50, jim stasheff <jds at math.upenn.edu> wrote:
>
>> The usual definition of Lie algebroid is in the context of a bundle L
--> M
>> with an anchor to the tangent bundle TM
>> Is there somewhere a definition of the purely algebraic analog? e.g.
with an anchor to Der(A) for some dga A?
>> jim
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