Standard bases for the universal associative conformal envelopes of Kac--Moody conformal algebras

TL;DR

This paper explicitly constructs a standard basis for the universal associative conformal envelope of a Kac--Moody conformal algebra's central extension at locality level 3, advancing understanding of conformal algebra structures.

Contribution

It provides the first explicit standard basis for the universal associative conformal envelope of a Kac--Moody conformal algebra's central extension at locality level 3.

Findings

Explicit standard basis of defining relations calculated.

Linear basis of free commutative conformal algebra obtained.

Enhanced understanding of conformal algebra structures at locality level 3.

Abstract

We study the universal enveloping associative conformal algebra for the central extension of a current Lie conformal algebra at the locality level $N=3$. A standard basis of defining relations for this algebra is explicitly calculated. As a corollary, we find a linear basis of the free commutative conformal algebra relative to the locality $N=3$ on the generators.