单点扩张代数的表示维数

doi:10.6040/j.issn.1671-9352.0.2016.086

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 85-91.doi: 10.6040/j.issn.1671-9352.0.2016.086

单点扩张代数的表示维数

孙维昆,林汉兴

天津职业技术师范大学理学院, 天津 300222

收稿日期:2016-03-07 出版日期:2016-06-20 发布日期:2016-06-15
作者简介:孙维昆(1976— ), 男, 博士, 副教授, 研究方向为计算机代数. E-mail:sunweikun@tute.edu.cn
基金资助:
天津市自然科学基金(14JCYBJC43100);天津职业技术师范大学科研基金(KJY14-06,KJ12-01)

Representation dimension of one-point extension algebras

SUN Wei-kun, LIN Han-xing

School of Science, Tianjin University of Technology and Education, Tianjin 300222, China

Received:2016-03-07 Online:2016-06-20 Published:2016-06-15

摘要/Abstract

摘要： 设A是一个表示无限型的Artin代数,M是一个左A模,Λ是A通过M得到的单点扩张代数。如果Fac(M)是tilting torsion类,且M是A的某个Auslander生成子的直和项,那么Λ的表示维数不超过A的表示维数,与A的整体维数加2两者的最大值。若M是APR-tilting模或者是BB-tilting模的投射部分,可以证明上述结论对由这两类模所得的单点扩张代数亦成立。

关键词: 单点扩张, 倾斜模, 表示维数

Abstract: Let A be a representation-infinite Artin algebra and M be a left A-module. Let Λ be the one-point extension algebra of A. If Fac(M)is a tilting torsion class and also that M is a direct summand of an Auslander generator about A, then the representation dimension of Λ is not greater than the maximum of representation dimension of A and global dimension of A plus 2. If M is an APR-tilting module or the projective part of a BB-tilting module, the conclusion still holds.

Key words: tilting modules, representation dimension, one-point extension

中图分类号:

O154.2

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.

SUN Wei-kun, LIN Han-xing. Representation dimension of one-point extension algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 85-91.

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单点扩张代数的表示维数

Representation dimension of one-point extension algebras

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