Homotopy Lie algebras. (English) Zbl 0823.18004

Hinich, Vladimir; Schechtman, Vadim

Gelfand, Sergej (ed.) et al., I. M. Gelfand seminar. Part 2: Papers of the Gelfand seminar in functional analysis held at Moscow University, Russia, September 1993. Providence, RI: American Mathematical Society. Adv. Sov. Math. 16(2), 1-28 (1993).

The authors use the notion of a module over an operad algebra with respect to an abelian tensor category to define homotopy Lie algebras as algebras over certain standard Lie operads. The homology groups of the standard chain complex of such an algebra are certain Tor groups. The total complex of a cosimplicial Lie algebra admits a structure of a Lie May algebra.
For the entire collection see [Zbl 0777.00036].

Reviewer: W.Grölz (Ammerbuch)

MSC:

18D35	Structured objects in a category (MSC2010)
18G35	Chain complexes (category-theoretic aspects), dg categories
55U35	Abstract and axiomatic homotopy theory in algebraic topology
17B55	Homological methods in Lie (super)algebras

Keywords:

operad algebra; abelian tensor category; homotopy Lie algebras; homology groups; standard chain complex; Lie May algebra