Rigidity of graded regular algebras

DOI10.1090/S0002-9947-08-04571-6zbMath1185.16043arXiv0706.0662OpenAlexW1989392145MaRDI QIDQ3542006

Ellen E. Kirkman, James J. Kuzmanovich, James J. Zhang

Publication date: 27 November 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0662

zbMATH Keywords

group actionsHilbert seriesreflectionstracesgeneralized Weyl algebrasArtin-Schelter regular algebrasquantum polynomial ringsfixed subringsNoetherian graded regular rings

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Graded rings and modules (associative rings and algebras) (16W50) Rings of differential operators (associative algebraic aspects) (16S32)

Related Items (24)

Semisimple reflection Hopf algebras of dimension sixteen ⋮ Invariant theory of Artin-Schelter regular algebras: a survey ⋮ Quantum binary polyhedral groups and their actions on quantum planes ⋮ Gorenstein subrings of invariants under Hopf algebra actions. ⋮ The discriminant criterion and automorphism groups of quantized algebras. ⋮ Local cohomology associated to the radical of a group action on a Noetherian algebra ⋮ Noncommutative Noether's problem vs classic Noether's problem ⋮ Generalized gorensteinness and a homological determinant for preprojective algebras ⋮ Reflection groups and rigidity of quadratic Poisson algebras ⋮ Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras. ⋮ Auslander's theorem for group coactions on Noetherian graded down-up algebras ⋮ Auslander’s Theorem for permutation actions on noncommutative algebras ⋮ Three infinite families of reflection Hopf algebras ⋮ Properties of the fixed ring of a preprojective algebra ⋮ Shephard-Todd-Chevalley theorem for skew polynomial rings. ⋮ Nakayama automorphism and rigidity of dual reflection group coactions ⋮ Rigidity of down-up algebras with respect to finite group coactions ⋮ Noncommutative Auslander theorem ⋮ Double extension regular algebras of type (14641). ⋮ Degree bounds for Hopf actions on Artin-Schelter regular algebras ⋮ Quantum linear Galois orders ⋮ Pertinency of Hopf actions and quotient categories of Cohen-Macaulay algebras ⋮ Noncommutative complete intersections ⋮ Invariant theory of finite group actions on down-up algebras

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