Kirillov structures up to homotopy

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.

Change of title, improved introduction section and examples. Minor typos etc corrected. No major revision of the key results. 15 pages. Further comments welcomed

References in corpus (3)

• Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
• Representations of Homotopy Lie-Rinehart Algebras
• L-infinity Algebras From Multicontact Geometry

Cited by in corpus (1)

• The Local Structure of Generalized Contact Bundles