Nakayama automorphism and rigidity of dual reflection group coactions

DOI10.1016/j.jalgebra.2017.05.021zbMath1460.16009arXiv1605.01958OpenAlexW2963171451MaRDI QIDQ2012031

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

Publication date: 27 July 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01958

zbMATH Keywords

rigidityHilbert seriesFrobenius algebraNakayama automorphismfixed subringArtin-Schelter regular algebradual reflection groupgroup coaction

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) Connections of group theory with homological algebra and category theory (20J99) Homological dimension in associative algebras (16E10) Hopf algebras and their applications (16T05)

Related Items

A note on the discriminant of reflection Hopf algebras ⋮ Semisimple reflection Hopf algebras of dimension sixteen ⋮ On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables ⋮ Examples of non-semisimple Hopf algebra actions on Artin-Schelter regular algebras ⋮ Three infinite families of reflection Hopf algebras ⋮ Nakayama automorphism and rigidity of dual reflection group coactions ⋮ Rigidity of down-up algebras with respect to finite group coactions ⋮ Degree bounds for Hopf actions on Artin-Schelter regular algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Skew Calabi-Yau algebras and homological identities.
• Hopf actions and Nakayama automorphisms.
• Generator sets for the alternating group
• Alternating subgroups of Coxeter groups.
• Dualising complexes and twisted Hochschild (co)homology for Noetherian Hopf algebras.
• Shephard-Todd-Chevalley theorem for skew polynomial rings.
• Graded algebras of global dimension 3
• Rings with Auslander dualizing complexes
• Schubert polynomials and the nilCoxeter algebra
• Noncommutative projective schemes
• Existence theorems for dualizing complexes over non-commutative graded and filtered rings
• On weak crossed products, Frobenius algebras, and the weak Bruhat ordering.
• A rigidity theorem for finite group actions on enveloping algebras of semisimple Lie algebras
• Homological properties of Sklyanin algebras
• Nakayama automorphism and rigidity of dual reflection group coactions
• Noncommutative complete intersections
• Semisimple Hopf actions on commutative domains.
• Mystic reflection groups.
• Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups.
• Projectively simple rings.
• Finite dimensional Hopf actions on algebraic quantizations
• The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
• Nichols-Woronowicz model of coinvariant algebra of complex reflection groups.
• Gorenstein subrings of invariants under Hopf algebra actions.
• Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras
• Nakayama automorphism and applications
• Combinatorics of Coxeter Groups
• Group-Graded Rings, Smash Products, and Group Actions
• Rigidity of graded regular algebras
• Growth in groups: ideas and perspectives
• Finite Unitary Reflection Groups