REAL

Rationality of Hilbert series in noncommutative invariant theory

Domokos, Mátyás and Drensky, Vesselin (2017) Rationality of Hilbert series in noncommutative invariant theory. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. pp. 1-18. ISSN 0218-1967

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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. © 2017 World Scientific Publishing Company

Item Type: Article
Uncontrolled Keywords: unipotent subgroup; Tensor algebra; Schur function; Relatively free associative algebras; reductive group; rational representation; rational Hilbert series; Noncommutative invariant theory
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 20 Nov 2017 14:06
Last Modified: 20 Nov 2017 14:06
URI: http://real.mtak.hu/id/eprint/70001

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