\(\mathcal Q\)-manifolds and higher analogs of Lie algebroids. (English) Zbl 1260.53133

Voronov, Th. Th.

Kielanowski, Piotr (ed.) et al., XXIX workshop on geometric methods in physics, Białowieża, Poland, June 27 – July 3, 2010. Selected papers based on the presentations at the workshop. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0861-6/hbk). AIP Conference Proceedings 1307, 191-202 (2010).

Summary: We show how the relation between \(Q\)-manifolds and Lie algebroids extends to “higher” or “nonlinear” analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations on sections of a Lie algebroid. When the base is a point, we obtain a generalization of Lie superalgebras.
For the entire collection see [Zbl 1234.81018].

MSC:

53D17	Poisson manifolds; Poisson groupoids and algebroids
17B63	Poisson algebras

Keywords:

derived bracket; graded manifold; higher derived bracket; Lie algebroid; higher Lie 4 algebroid; \(\mathcal Q\)-manifold; strongly homotopy Lie algebra; supermanifold