Skew Calabi–Yau algebras and homological identities
Skew Calabi–Yau algebras and homological identities
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DOI：
10.1016/j.aim.2014.07.010
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发表时间：
2013-02
影响因子：
1.7
通讯作者：
M. Reyes;D. Rogalski;James J. Zhang
中科院分区：
文献类型：
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作者：
M. Reyes;D. Rogalski;James J. Zhang
斜Calabi-Yau代数是允许非平凡Nakayama自同构的Calabi-Yau代数的推广。证明了Nakayama自同构的三个同调恒等式，并给出了几个应用。我们证明的恒等式表明：（i）粉碎积代数A# H的Nakayama自同构如何与分次斜Calabi-Yau代数A和作用于它的有限维Hopf代数H的Nakayama自同构相关;（ii）A的分次扭转的Nakayama自同构如何与A的Nakayama自同构相关;当A是Noether、连通分次和Koszul代数时，斜Calabi-Yau代数A的Nakayama自同构具有平凡同调行列式.
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.