From \(L_{\infty }\)-algebroids to higher Schouten/Poisson structures. (English) Zbl 1237.53077

Bruce, Andrew James

Rep. Math. Phys. 67, No. 2, 157-177 (2011).

This paper deals with L\(_\infty \) algebroids and their description in terms of certain higher Schouten and Poisson structures. Let us recall that L\(_\infty \) algebroids arise naturally when one generalizes the Lie algebroid structure on \(T^*M\) for a Poisson manifold to the higher structures. In this paper, the author completes the framework found in the theory of higher Schouten and Poisson structures. He recalls some basic facts about graded manifolds and L\(_\infty \) algebroids. Then, he proves that these L\(_\infty \) algebroids can be understood in terms of \(Q\)-manifolds and described in terms of higher Schouten and Poisson structures on graded manifolds and graded supermanifolds. Some explicit examples are also given to illustrate the main results of the paper. Applications are finally discussed.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D17	Poisson manifolds; Poisson groupoids and algebroids
58A50	Supermanifolds and graded manifolds

Keywords:

L\(_\infty \)-algebroids; Schouten structures; Poisson structures; graded manifolds; Lie super algebras; Lie algebroids

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