Lie algebroids and homological vector fields. (English. Russian original) Zbl 0955.58017

Vaintrob, A. Yu.

Russ. Math. Surv. 52, No. 2, 428-429 (1997); translation from Usp. Mat. Nauk 52, No. 2, 161-162 (1997).

The notion of a Lie algebroid, introduced by J. Pradines, is an analogue of the algebra of a Lie group for differentiable groupoids. Lie algebroids combine the properties of Lie algebras and manifolds and are used in differential geometry, symplectic geometry, and representation theory.
The goal of this paper is to demonstrate that the theory of Lie algebroids is a special case of the theory of homological vector fields on supermanifolds and to indicate the possible applications of this approach.

MSC:

58H05	Pseudogroups and differentiable groupoids
58A50	Supermanifolds and graded manifolds
22A22	Topological groupoids (including differentiable and Lie groupoids)

Keywords:

Lie algebroids; homological vector fields; supermanifolds