戈伦斯坦投影模组内态代数的同调维数

IF 0.4 4区数学 Q4 MATHEMATICS

Czechoslovak Mathematical Journal Pub Date : 2024-08-28 DOI:10.21136/cmj.2024.0199-23

Aiping Zhang, Xueping Lei

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引用次数: 0

摘要

设 A 是具有戈伦斯坦-奥斯兰德生成器 E 的 CM 有限阿尔丁代数，M 是戈伦斯坦投影 A 模块，B = EndAM。此外，如果 A 在 2 ⩽ n < ∞ 时是 n-Gorenstein 的，那么我们将证明 B 的全局维度小于或等于 n 加上 HomA(M, E) 的 B 投影维度。作为应用，EndAE 的全局维度小于或等于 n。

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Homological dimensions for endomorphism algebras of Gorenstein projective modules

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = End_AM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of Hom_A(M, E). As an application, the global dimension of End_AE is less than or equal to n.