Standard Bases for the Universal Associative Conformal Envelopes of Kac–Moody Conformal Algebras

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.