2015/12/20 by M. Domokos, Vesselin Drensky, Domokos, M. +1
Mathematics · Physics and Astronomy · #05E10 (Secondary) #13A02 #13A50 #15A72 #16R10 (Primary) #16W22 #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1512.06411
openalex publication_date 2015/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 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.