τ-倾斜τ-1-倾斜模与1-Gorenstein代数

doi:10.6040/j.issn.1671-9352.0.2022.546

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 16-18.doi: 10.6040/j.issn.1671-9352.0.2022.546

τ-倾斜τ^-1-倾斜模与1-Gorenstein代数

张孝金(),陈宇轩*(),顾彪

江苏师范大学数学与统计学院, 江苏徐州 221116

收稿日期:2022-10-19 出版日期:2024-04-20 发布日期:2024-04-12
通讯作者: 陈宇轩 E-mail:xjzhang@jsnu.edu.cn;1481859952@qq.com
作者简介:张孝金(1983—)，男，教授，博士，研究方向为代数表示论. E-mail: xjzhang@jsnu.edu.cn
基金资助:
国家自然科学基金资助项目(12171207);江苏省大学生创新项目(202210320149Y)

τ-tilting τ^-1-tilting modules and 1-Gorenstein algebras

Xiaojin ZHANG(),Yuxuan CHEN*(),Biao GU

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China

Received:2022-10-19 Online:2024-04-20 Published:2024-04-12
Contact: Yuxuan CHEN E-mail:xjzhang@jsnu.edu.cn;1481859952@qq.com

摘要/Abstract

摘要：

证明具有τ-倾斜τ^-1-倾斜模T的代数A的同调性质, 推广1-Gorenstein代数的性质。给出例子说明代数A未必为1-Gorenstein代数。

关键词: Gorenstein代数, τ-倾斜模, τ^-1-倾斜模

Abstract:

For an algebra A admitting a τ-tilting τ^-1-tilting module T, some homological properties of A are given, which generalize the homological properties of 1-Gorenstein algebras. Moreover, it is shown that A is not necessarily to be a 1-Gorenstein algebra.

Key words: Gorenstein algebra, τ-tilting module, τ^-1-tilting module

中图分类号:

O154.2

张孝金,陈宇轩,顾彪. τ-倾斜τ^-1-倾斜模与1-Gorenstein代数[J]. 《山东大学学报(理学版)》, 2024, 59(4): 16-18.

Xiaojin ZHANG,Yuxuan CHEN,Biao GU. τ-tilting τ^-1-tilting modules and 1-Gorenstein algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 16-18.

参考文献 6

1	HAPPEL D . On Gorenstein algebra[M]. Basel: Birkhauser Verlag, 1991.
2	ADACHI T , IYAMA O , REITEN I . τ-tilting theory[J]. Compositio Mathematica, 2014, 150, 415- 452. doi: 10.1112/S0010437X13007422
3	XIE Zongzhen , ZAN Libo , ZHANG Xiaojin . Three results for τ-rigid modules[J]. Rocky Mountain Journal of Mathematics, 2019, 49 (8): 2791- 2807.
4	HAPPEL D , RINGEL C M . Tilted algebras[J]. Transactions of the American Mathematical Society, 1982, 274 (2): 399- 443. doi: 10.1090/S0002-9947-1982-0675063-2
5	GENG Yuxian , DING Nanqing . W-Gorenstein modules[J]. Journal of Algebra, 2011, 325 (1): 132- 146. doi: 10.1016/j.jalgebra.2010.09.040
6	ZHANG Xiaojin . Self-orthogonal τ-tilting modules and tilting modules[J]. Journal of Pure and Applied Algebra, 2022, 226 (3): 10680.

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[1]	陈文倩,张孝金,昝立博. Gorenstein代数上的倾斜模的个数[J]. 山东大学学报（理学版）, 2018, 53(10): 14-16.
[2]	章璞. Gorenstein投射模[J]. J4, 2009, 44(2): 1-13.

τ-倾斜τ^-1-倾斜模与1-Gorenstein代数

τ-tilting τ^-1-tilting modules and 1-Gorenstein algebras

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τ-倾斜τ-1-倾斜模与1-Gorenstein代数

τ-tilting τ-1-tilting modules and 1-Gorenstein algebras

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τ-倾斜τ^-1-倾斜模与1-Gorenstein代数

τ-tilting τ^-1-tilting modules and 1-Gorenstein algebras