Associative algebras related to conformal algebras

TL;DR

This paper introduces TC-algebras, a new class related to conformal algebras, encompassing Weyl algebras and their subalgebras, and applies structure theory to describe them.

Contribution

It defines TC-algebras and connects them to conformal algebras, providing a structural description based on recent conformal algebra theory.

Findings

TC-algebras include Weyl algebras and subalgebras

Structural descriptions of TC-algebras are obtained

Applications of conformal algebra theory to TC-algebras

Abstract

In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TC-algebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we generally mean what is known as $H$-pseudo-algebra over the polynomial Hopf algebra $H=\Bbbk[T_1,..., T_n]$. Some recent results in structure theory of conformal algebras are applied to get a description of TC-algebras.