Odd Jacobi manifolds and Loday-Poisson brackets
Mathematical Physics
2014-04-11 v2 Differential Geometry
math.MP
Quantum Algebra
Symplectic Geometry
Abstract
In this paper we construct a non-skewsymmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi structure and the Loday-Poisson structure. Furthermore, we show that the Loday-Poisson bracket satisfies the Leibniz rule over the noncommutative product derived from the homological vector field.
Keywords
Cite
@article{arxiv.1301.4799,
title = {Odd Jacobi manifolds and Loday-Poisson brackets},
author = {Andrew James Bruce},
journal= {arXiv preprint arXiv:1301.4799},
year = {2014}
}
Comments
18 pages. Further comments added and slight rearrangement of the material. No major changes to the mathematical content. Comments welcomed