On irreducible algebras of conformal endomorphisms over a linear algebraic group

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 where G is finite. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra, 2008.