Hochschild cohomology of the universal associative conformal envelope of the Virasoro Lie conformal algebra with coefficients in all finite modules

TL;DR

This paper computes the Hochschild cohomology of the universal associative conformal envelope of the Virasoro Lie conformal algebra, using algebraic discrete Morse theory and Gr"obner--Shirshov basis methods.

Contribution

It introduces a novel approach to calculating Hochschild cohomology for this algebra using advanced algebraic and combinatorial techniques.

Findings

Hochschild cohomology groups are explicitly determined.

Construction of Anick resolution for the algebra.

Application of algebraic discrete Morse theory and Gr"obner--Shirshov basis.

Abstract

In this paper, we find the Hochschild cohomology groups of the universal associative conformal envelope $U(3)$ of the Virasoro Lie conformal algebra with respect to associative locality $N=3$ on the generator with coefficients in all finite modules. In order to obtain this result, we construct the Anick resolution via the algebraic discrete Morse theory and Gr\"obner--Shirshov basis.