A Lie Group Structure Underlying the Triplectic Geometry

TL;DR

This paper reveals that the structure of compatible antibrackets in triplectic geometry encodes an underlying Lie group structure, generalizing previous axioms and linking antibrackets to invariant vector fields.

Contribution

It demonstrates that triplectic antibrackets correspond to Lie group structures, extending the understanding of their algebraic and geometric foundations.

Findings

Antibrackets encode a Lie group structure

Standard triplectic axioms correspond to Abelian groups

Antibrackets relate to invariant vector fields on the group

Abstract

We consider the pair of degenerate compatible antibrackets satisfying a generalization of the axioms imposed in the triplectic quantization of gauge theories. We show that this actually encodes a Lie group structure, with the antibrackets being related to the left- and right- invariant vector fields on the group. The standard triplectic quantization axioms then correspond to Abelian groups.