Cohomology of tails, Tate–Vogel cohomology, and noncommutative Serre duality over Koszul quiver algebras☆
Cohomology of tails, Tate–Vogel cohomology, and noncommutative Serre duality over Koszul quiver algebras☆
复制标题
尾部上同调、Tate–Vogel 上同调以及 Koszul quiver 代数上的非交换 Serre 对偶性☆
DOI：
10.1016/j.jalgebra.2004.05.017
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发表时间：
2004
影响因子：
0.9
通讯作者：
A. Martsinkovsky
中科院分区：
文献类型：
--
作者：
R. Villa;A. Martsinkovsky
本文的主要结果表明，在颤栗代数之间的Koszul对偶下，尾的上同调是用梯度Vogel上同调来识别的。作为应用，给出了广义Artin-Schelter正则Koszul颤代数上非交换Serre对偶性的一个新的证明。它是从任意（即不一定是Koszul） Frobenius代数上的类似公式推导出来的，该公式与Auslander-Reiten公式等效。作为另一个应用，证明了在广义Artin-Schelter正则Koszul颤动代数上，非交换Serre对偶公式中出现的任何代数自同构在Koszul对偶下与Koszul-对偶代数的中山自同构密切相关。
The main result of the paper shows that, under Koszul duality between quiver algebras, cohomology of tails is identified with graded Vogel cohomology. As an application, a new proof of the noncommutative Serre duality over generalized Artin–Schelter regular Koszul quiver algebras is given. It is deduced from a similar formula over an arbitrary (i.e., not necessarily Koszul) Frobenius algebra, which turns out to be equivalent to the Auslander–Reiten formula. As another application, it is shown that, over a generalized Artin–Schelter regular Koszul quiver algebra, any algebra automorphism appearing in the noncommutative Serre duality formula is closely related, under Koszul duality, to the Nakayama automorphism of the Koszul-dual algebra.