Higher derived brackets for arbitrary derivations. (English) Zbl 1136.17014

Voronov, Theodore Th.

Molitor-Braun, Carine (ed.) et al., Proceedings of the 4th conference on Poisson geometry, Luxembourg, June 7–11, 2004. Luxembourg: Université du Luxembourg (ISBN 2-87971-253-X/pbk). Travaux Mathématiques 16, 163-186 (2005).

Higher derived brackets are introduced by the author in a work motivated by physical and differential geometric examples [J. Pure Appl Algebra 202, No. 1–3, 133–153 (2004; Zbl 1086.17012)]. Here higher derived brackets generated by an arbitrary derivation of a Lie superalgebra are introduced and studied.
An important result states that the jacobiators for the higher derived brackets generated by an odd derivation \(D\) are equal to the brackets generated by \(D^2\). It is also established a relation between higher derived brackets and homotopical algebra giving an alternative approach to higher derived brackets.
For the entire collection see [Zbl 1085.53003].

Reviewer: Georges Hoff (Villetaneuse)

MSC:

17B40	Automorphisms, derivations, other operators for Lie algebras and super algebras
18G55	Nonabelian homotopical algebra (MSC2010)

Keywords:

Lie superalgebra; derivation; derived bracket; Jacobiator

Citations:

Zbl 1086.17012