Notes on the Super Nambu Bracket
M. Sakakibara
TL;DR
This paper introduces a super Nambu-Poisson algebra on super manifolds, proposing a new skew-symmetric property for the super Nambu bracket and linking divergence of super Nambu-Hamiltonian vector fields to a generalized Batalin-Vilkovisky algebra.
Contribution
It defines a super Nambu-Poisson algebra with a novel skew-symmetry and connects divergence of super Nambu-Hamiltonian vector fields to a generalized BV algebra.
Findings
Defined super Nambu-Poisson algebra on super manifolds
Proposed a new skew-symmetric property for super Nambu brackets
Connected divergence of super Nambu-Hamiltonian vector fields to a generalized BV algebra
Abstract
We define a super Nambu-Poisson algebra over a super manifold. A super Nambu bracket does not satisfy the usual skew-symmetric property, and we propose another skew-symmetric property. We show that the divergence of super Nambu-Hamiltonian vector fields leads to a generalization of the Batalin-Vilkovisky algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology