On the tensor structure of BRST differential and it's application

TL;DR

This paper explores the tensor structure of the BRST differential, deriving generalized algebra differentials that extend classical cohomological tools, with potential applications in mathematical physics.

Contribution

It introduces tensor representations of the BRST differential and defines new $CL_{infty}$ and $GA_{infty}$ differentials as generalizations of known algebraic differentials.

Findings

Tensor structure of BRST differential computed

Defined $CL_{infty}$ and $GA_{infty}$ differentials

Extended classical cohomological differentials to new algebraic frameworks

Abstract

In this paper,we compute tensor structure of BRST differential and use this tensor representation we give out $CL_{\infty}$ algebra differential and $GA_{\infty}$ differential which are generalization of Chevalley-Eilenberg differential and Hochchild differential respectively.