Higher Derived Brackets for Arbitrary Derivations
Abstract
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathematical physics. From a totally different viewpoint, we show that higher derived brackets arise when one wants to turn the inclusion map of a subalgebra of a differential Lie superalgebra, with a given complementary subalgebra, into a fibration. (For a non-Abelian complementary subalgebra, this leads to a generalization of -algebras with dropped or weakened (anti)symmetry of the brackets.)
Cite
@article{arxiv.math/0412202,
title = {Higher Derived Brackets for Arbitrary Derivations},
author = {Theodore Th. Voronov},
journal= {arXiv preprint arXiv:math/0412202},
year = {2019}
}
Comments
24 pages. LaTeX 2e. In the second version a minor style editing was done. Uses a package for commutative diagrams, diagrams.sty, available at ftp://ftp.dante.de/pub/tex/macros/generic/diagrams/taylor/ Extra editing (style, misprints...) in the third version