Skew Calabi-Yau Algebras and Homological Identities
arXiv:1302.0437 · doi:10.1016/j.aim.2014.07.010
Abstract
A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A # H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A and a finite-dimensional Hopf algebra H that acts on it; (ii) how the Nakayama automorphism of a graded twist of A is related to the Nakayama automorphism of A; and (iii) that Nakayama automorphism of a skew Calabi-Yau algebra A has trivial homological determinant in case A is noetherian, connected graded, and Koszul.
39 pages; minor changes, mostly in the Introduction
References in corpus (6)
Cited by in corpus (46)
- Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras
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- McKay Correspondence for semisimple Hopf actions on regular graded algebras, II
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- Note on Nakayama automorphisms of PBW deformations and Hopf actions
- PBW deformations of Artin-Schelter regular algebras
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- An introduction to Noncommutative Projective Geometry
- The Zariski cancellation problem for Poisson algebras
- AS-regularity of geometric algebras of plane cubic curves
- On quantum groups associated to non-Noetherian regular algebras of dimension 2
- A new family of Poisson algebras and their deformations
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- The classification of 3-dimensional noetherian cubic Calabi-Yau algebras
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- The structure of connected (graded) Hopf algebras
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- New Artin-Schelter regular and Calabi-Yau algebras via normal extensions
- Algebraic structures in comodule categories over weak bialgebras
- Automorphism groupoids in noncommutative projective geometry
- Nakayama automorphism and applications
- Group-Graded Twisted Calabi--Yau Algebras
- Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity
- Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras
- A complete classification of -dimensional quadratic AS-regular algebras of Type EC
- Four-vertex quivers supporting twisted graded Calabi-Yau algebras
- Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras
- Nakayama automorphisms of twisted tensor products
- Skew Calabi-Yau property of normal extensions
- Hopf-Galois objects of Calabi-Yau Hopf algebras
- On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables
- Nakayama automorphism of quasi-commutative skew PBW extensions over AS-regular algebras
- The Classification of 3-Calabi-Yau algebras with 3 generators and 3 quadratic relations
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- The Jacobian, reflection arrangement and discriminant for reflection Hopf algebras
- Cleft extensions of Koszul twisted Calabi-Yau algebras
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- Noncommutative cyclic isolated singularities