Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras
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DOI：
10.1090/tran/6640
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发表时间：
2014-08
期刊：
arXiv: Rings and Algebras
影响因子：
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通讯作者：
M. Reyes;D. Rogalski;James J. Zhang
M. Reyes;D. Rogalski;James J. Zhang
中科院分区：
其他
文献类型：
--
作者：
M. Reyes;D. Rogalski;James J. Zhang

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我们研究了使(三角)范畴中对象的Ext-代数成为Frobenius代数的充分条件，并计算了相应的Nakayama自同构。作为应用，我们证明了对任意Notherian Artin-Schelter正则(从而斜Calabi-Yau)代数A，hdet($\MU_A$)=1。
We investigate the conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that hdet($\mu_A$) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.