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arXiv · 1302.0437

Skew Calabi-Yau Algebras and Homological Identities

Manuel Reyes·Daniel Rogalski·James J. Zhang
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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.

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BibTeXRIS

Manuel Reyes, Daniel Rogalski, James J. Zhang. 2013-02-16. Skew Calabi-Yau Algebras and Homological Identities. https://doi.org/10.1016/j.aim.2014.07.010

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