Gorenstein代数上的倾斜模的个数

doi:10.6040/j.issn.1671-9352.0.2017.654

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (10): 14-16.doi: 10.6040/j.issn.1671-9352.0.2017.654

Gorenstein代数上的倾斜模的个数

陈文倩,张孝金^*,昝立博

南京信息工程大学数学与统计学院, 江苏南京 210044

收稿日期:2017-12-28 出版日期:2018-10-20 发布日期:2018-10-09
作者简介:陈文倩(1994— )女,硕士研究生,研究方向为代数表示论. E-mail:chenwenqianaa@163.com*通信作者简介:张孝金(1983— )男, 博士,副教授, 研究方向为代数表示论. E-mail:xjzhang@nuist.edu.cn
基金资助:
国家自然科学基金资助项目(11571164,11671174);江苏省自然科学基金资助项目(BK20130983)

The number of tilting modules over Gorenstein algebras

CHEN Wen-qian, ZHANG Xiao-jin^*, ZAN Li-bo

School of Mathematics and Statistics, Nanjing University of Information Science &
Technology, Nanjing 210044, Jiangsu, China

Received:2017-12-28 Online:2018-10-20 Published:2018-10-09

摘要/Abstract

摘要： 若A是一个Gorenstein代数,则倾斜右A-模的个数等于倾斜左A-模的个数。给出反例说明自内射维数大于等于2的Gorenstein代数B的经典倾斜右B-模的个数不一定等于经典倾斜左B-模的个数。

关键词: Gorenstein代数, 倾斜模, 余倾斜模

Abstract: For a Gorenstein algebra A, the number of tilting right A-modules is equal to the number of tilting left A-modules. A counter-example is given to show that for a Gorenstein algebra B with self-injective dimension no less than 2, the number of classical tilting left B-modules is not necessary to be equal to that of classical tilting right B-modules.

Key words: Gorenstein algebra, tilting module, cotilting module

中图分类号:

O154.2

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.

CHEN Wen-qian, ZHANG Xiao-jin, ZAN Li-bo. The number of tilting modules over Gorenstein algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 14-16.

参考文献 10

[1]	BERNSTEIN J, GELFAND I M, PONIMAREV V. Coxeter functors and Gabriels theorem[J]. Russian Mathematical Surveys, 1973, 28(2):17-32.
[2]	HAPPEL D, RINGEL C M. Tilted algebras[J]. Transactions in the American Mathematical Society, 1982, 274(2):399-443.
[3]	MIYASHITA Y. Tilting modules of finite projective dimension[J]. Mathematische Zeitschrift, 1986, 193:113-146.
[4]	ASSEM I, SIMSON D, SKOWRONSKI A. Elements of the representation theory of associative algebras: Vol.1[M]. Cambridge: Cambridge University Press, 2011.
[5]	AUSLANDER M, SOLBERG O. Gorenstein algebras and algebras with dominant dimension at least 2[J]. Communications in Algebra, 1993, 21(11):3897-3934.
[6]	ANGELERI-HUGEL L, HAPPEL D, KRAUSE H. Handbook of tilting theory[M]. Cambridge: Cambridge University Press, 2007: 1-484.
[7]	CHEN H X, XI C C. Dominant dimensions, derived equivalences and tilting modules[J]. Israel Journal of Mathematics, 2016, 215:349-395.
[8]	IYAMA O, ZHANG X J. Classifying τ-tilting modules over the Auslander algebra of K[x] /(xn)[J/OL]. ArXiv: 1602. 05037. http://cn.arxiv.org/abs/1602.05037.
[9]	NGUYEN V C, REITEN I, TODOROV G, et al. Dominant dimension and tilting modules[J]. Mathematische Zeitschrift, 2018: 1-27.
[10]	ZAKS A. Injective dimension of semiprimary rings[J]. Journal of Algebra, 1969, 13:73-86.

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Gorenstein代数上的倾斜模的个数

The number of tilting modules over Gorenstein algebras

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