一类Auslander代数的倾斜模的个数

doi:10.6040/j.issn.1671-9352.0.2019.388

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (4): 74-76.doi: 10.6040/j.issn.1671-9352.0.2019.388

• • 上一篇

一类Auslander代数的倾斜模的个数

昝立博¹,张孝金^2*

1.南京信息工程大学数学与统计学院, 江苏南京 210044;2.江苏师范大学数学与统计学院, 江苏徐州 221116

发布日期:2020-04-09
作者简介:昝立博(1978— ),女,博士,研究方向为环与代数. E-mail:zanlibo@nuist.edu.cn*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理论. E-mail:xjzhangmaths@163.com
基金资助:
国家自然科学基金资助项目(11671174)

Number of tilting modules over a class of Auslander algebras

ZAN Li-bo¹, ZHANG Xiao-jin^2*

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China

Published:2020-04-09

摘要/Abstract

摘要： 证明了A_n型的根平方为零的代数的Auslander代数的经典倾斜模的个数是2^n-1。

关键词: Auslander代数, 根方为零代数, 倾斜模

Abstract: For a radical square zero algebra B of type A_n, the number of tilting modules over the Auslander algebra of B is 2^n-1.

Key words: Auslander algebra, radical square zero algebra, tilting module

中图分类号:

O154.2

昝立博,张孝金. 一类Auslander代数的倾斜模的个数[J]. 《山东大学学报(理学版)》, 2020, 55(4): 74-76.

ZAN Li-bo, ZHANG Xiao-jin. Number of tilting modules over a class of Auslander algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 74-76.

[1] HAPPEL D, RINGEL C M. Tilted algebras[J]. Transactions of the American Mathematical Society, 1982, 274:399-443.
[2] AUSLANDER M, REITEN I, SMALO S O. Representation theory of Artin algebras[C] //Cambridge Studies in Advanced Mathematics, 36. Cambridge: Cambridge University Press, 1997.
[3] BRUSTLE T, HILLE L, RINGEL C M, et al. The Δ-filtered modules without self-extensions for the Auslander algebra of K[x] /(xⁿ)[J]. Algebra Representation Theory, 1999, 2:295-312.
[4] KAJITA N. The number of tilting modules over hereditary algebras and tilting modules over Auslander algebras[D]. Nagoya: Nagoya University, 2008.
[5] ADACHI T, IYAMA O, REITEN I. τ-tilting theory [J]. Compositio Mathematica, 2014, 150:415-452.
[6] IYAMA O, ZHANG X J. Classifying τ-tilting modules over the Auslander algebra of K[x] /(xⁿ)[J]. Journal of the Mathematical Society of Japan, http://arxiv.org/abs/1602.05037.
[7] IYAMA O, ZHANG X J. Tilting modules over Auslander-Gorenstein algebras[J]. Pacific Journal of Mathematics, 2019, 298(2):399-416.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

一类Auslander代数的倾斜模的个数

Number of tilting modules over a class of Auslander algebras

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

多维度评价

本文评价

推荐阅读 0

[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]	孙维昆,林汉兴. 单点扩张代数的表示维数[J]. 山东大学学报（理学版）, 2016, 51(6): 85-91.
[3]	雷雪萍. 几乎C-倾斜模[J]. J4, 2011, 46(2): 101-104.
[4]	雷雪萍. WC倾斜模的AuslanderReiten对应[J]. J4, 2009, 44(12): 41-43.
[5]	雷雪萍 . W-C-倾斜模[J]. J4, 2008, 43(10): 27-30 .