$G$-Algebra Structure on the Higher Order Hochschild Cohomology $H^*_{S^2}(A,A)$

TL;DR

This paper develops a deformation theory linked to higher Hochschild cohomology on the 2-sphere and investigates a G-algebra structure related to this theory, advancing understanding of algebraic structures in cohomology.

Contribution

It introduces a deformation framework for higher Hochschild cohomology and explores the associated G-algebra structure, which is a novel connection in this context.

Findings

Established a deformation theory for $H_{S^2}^*(A,A)$

Identified a G-algebra structure related to the deformation theory

Enhanced understanding of algebraic structures in higher Hochschild cohomology

Abstract

We present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory.