Graded associative conformal algebras of finite type

TL;DR

This paper classifies simple and semisimple graded associative conformal algebras of finite type, which include pseudo-algebras over certain Hopf algebras related to linear algebraic groups.

Contribution

It provides a classification of simple and semisimple graded associative conformal algebras of finite type, expanding understanding of their structure and relation to algebraic groups.

Findings

Classification of simple graded associative conformal algebras.

Classification of semisimple graded associative conformal algebras.

Connection to pseudo-algebras over Hopf algebras of algebraic groups.

Abstract

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\simeq \Gamma $. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained.