Morse matching method for conformal cohomologies

TL;DR

This paper introduces a Morse matching method to compute conformal cohomologies, specifically applying discrete algebraic Morse theory to Hochschild cohomologies of associative conformal algebras, exemplified by the Virasoro algebra.

Contribution

It presents a novel application of Morse theory to conformal algebra cohomology computations, providing explicit dimension calculations for the universal associative conformal envelope.

Findings

Computed the dimensions of the universal associative conformal envelope U(3) for the Virasoro algebra.

Demonstrated the effectiveness of Morse matching in simplifying cohomology calculations.

Provided a new computational approach for associative conformal algebra cohomologies.

Abstract

We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the universal associative conformal envelope $U(3)$ of the Virasoro Lie conformal algebra relative to the associative locality $N=3$ on the generator with scalar coefficients.