Kirillov structures up to homotopy

Andrew James Bruce; Alfonso G. Tortorella

doi:10.1016/j.difgeo.2016.06.005

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arXiv · 1507.00454

Kirillov structures up to homotopy

Andrew James Bruce·Alfonso G. Tortorella

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Abstract

We present the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak of higher Jacobi brackets. These brackets are understood furnishing the module of sections with an $L_{\infty}$-algebra, which we refer to as a homotopy Kirillov algebra. We are then to higher Kirillov algebroids as higher generalisations of Jacobi algebroids. Furthermore, we show how to associate a higher Kirillov algebroid and a homotopy BV-algebra with every higher Kirillov manifold. In short, we construct homotopy versions of some of the well-known theorems related to Kirillov's local Lie algebras.

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BibTeX RIS

Andrew James Bruce, Alfonso G. Tortorella. 2016-02-15. Kirillov structures up to homotopy. https://doi.org/10.1016/j.difgeo.2016.06.005

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