Rationality of Hilbert series in noncommutative invariant theory

Author:

Domokos Mátyás1,Drensky Vesselin2

Affiliation:

1. MTA Alfréd Rényi Institute of Mathematics, Reáltanoda Utca 13-15, 1053 Budapest, Hungary

2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria

Abstract

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has a rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

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