On irreducible algebras of conformal endomorphisms over a linear algebraic group

TL;DR

This paper investigates the structure of conformal endomorphism algebras over a linear algebraic group, revealing how irreducible subalgebras generate essential ideals, especially in the finite group case.

Contribution

It characterizes irreducible conformal subalgebras and their generated ideals within the algebra of conformal endomorphisms over algebraic groups.

Findings

Irreducible conformal subalgebras generate essential left ideals when combined with multiplication operators.

The structure of such subalgebras is described explicitly for finite groups.

Provides a classification of conformal subalgebras acting irreducibly over algebraic groups.

Abstract

We study the algebra of conformal endomorphisms $\Cend^{G,G}_n$ of a finitely generated free module $M_n$ over the coordinate Hopf algebra $H$ of a linear algebraic group $G$. It is shown that a conformal subalgebra of $\Cend_n$ acting irreducibly on $M_n$ generates an essential left ideal of $\Cend^{G,G}_n$ if enriched with operators of multiplication on elements of $H$. In particular, we describe such subalgebras for the case when $G$ is finite.