Skew Calabi–Yau algebras and homological identities

By Manuel Reyes, D. Rogalski, James J. Zhang. 2013

133 citations recorded by the source corpus.

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 the Nakayama automorphism of a skew Calabi–Yau algebra A has trivial homological determinant in case A is noetherian, connected graded, and Koszul.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e59c57a373352af6977542edc1988cd8f90742c7

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In Algebra and Number Theory

1. D. Rogalski
2. Manuel Reyes
3. James J. Zhang
4. U. Krähmer
5. Amnon Yekutieli
6. Kenneth A. Brown

In Geometry and Topology

1. D. Rogalski
2. Manuel Reyes
3. James J. Zhang
4. Amnon Yekutieli
5. U. Krähmer
6. Kenneth A. Brown
7. Masaki Kashiwara

In Mathematical Physics

1. D. Rogalski
2. Manuel Reyes
3. James J. Zhang
4. Amnon Yekutieli
5. Masaki Kashiwara

Citations in the corpus

• Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras (2014, background): “AS for short) Gorenstein kalgebras. By studying the Ext-algebras of objects in these categories we will obtain several interesting consequences for such Gorenstein algebras. This paper is a sequel to [RRZ]. In particular, we make significant progress on a conjecture in [RRZ] about the homological det”