Title:
**MC
Elements in Pronilpotent** **DG
Lie Algebras **

Authors:
Amnon Yekutieli

Publication status:
*J.
Pure Appl. Algebra*
**216**
(2012),
2338–2360

Abstract:

Consider a pronilpotent DG (differential graded) Lie algebra
over a field of characteristic 0. In the first part of the paper we
introduce the reduced Deligne groupoid associated to this DG Lie
algebra. We prove that a DG Lie quasi-isomorphism between two such
algebras induces an equivalence between the corresponding reduced
Deligne groupoids. This extends the famous result of Goldman- Millson
(attributed to Deligne) to the unbounded pronilpotent case.

In
the second part of the paper we consider the Deligne 2-groupoid. We
show it exists under more relaxed assumptions than known before (the
DG Lie algebra is either nilpotent or of quasi quantum type). We
prove that a DG Lie quasi-isomorphism between such DG Lie algebras
induces a weak equivalence between the corresponding Deligne
2-groupoids.

In the third part of the paper we prove that an
L-infinity quasi-isomorphism between pronilpotent DG Lie algebras
induces a bijection between the sets of gauge equivalence classes of
Maurer-Cartan elements. This extends a result of Kontsevich and
others to the pronilpotent case.

Electronic
Preprint:

paper
(pdf)

updated 15 Sep 2012