Antibrackets and non-Abelian equivariant cohomology

TL;DR

This paper explores the use of antibrackets within the Weil algebra of semisimple Lie groups and symplectic manifolds to develop models for non-Abelian equivariant cohomologies.

Contribution

It introduces a novel application of antibrackets to formulate models of non-Abelian equivariant cohomologies using algebraic structures.

Findings

Antibrackets are effectively applied to Weil algebra and symplectic algebra.

New models for non-Abelian equivariant cohomologies are formulated.

The approach bridges algebraic structures with topological invariants.

Abstract

The Weil algebra of a semisimple Lie group and an exterior algebra of a symplectic manifold possess antibrackets. They are applied to formulate the models of non--abelian equivariant cohomologies.