The graded Jacobi algebras and (co)homology
Abstract
Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.
Keywords
Cite
@article{arxiv.math/0207017,
title = {The graded Jacobi algebras and (co)homology},
author = {Janusz Grabowski and Giuseppe Marmo},
journal= {arXiv preprint arXiv:math/0207017},
year = {2008}
}
Comments
20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Gen