This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-
Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new …

This paper provides a conceptual study of the twisting procedure, which amounts to create
functorially new differential graded Lie algebras, associative algebras or operads (as well as …

In this review article, first we give the concrete formulas of representations and
cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and …

This book brings together both the classical and current aspects of deformation theory. The
presentation is mostly self-contained, assuming only basic knowledge of commutative …

arXiv:math/0507284v1 [math.AG] 14 Jul 2005 Page 1 arXiv:math/0507284v1 [math.AG] 14 Jul
2005 Deformation theory via differential graded Lie algebras Marco Manetti, Universit`a di …

This is the first in a series of articles devoted to deformation quantization of gerbes. We
introduce basic definitions, interpret deformations of a given stack as Maurer–Cartan …

First three sections of this overview paper cover classical topics of deformation theory of
associative algebras and necessary background material. We then analyze algebraic …

We define a simplicial enrichment on the category of differential graded Hopf cooperads (the
category of dg Hopf cooperads for short). We prove that our simplicial enrichment satisfies …

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an
isomorphism between invariant polynomials of a Lie algebra and the center of its universal …