JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 85-91.doi: 10.6040/j.issn.1671-9352.0.2016.086

Previous Articles     Next Articles

Representation dimension of one-point extension algebras

SUN Wei-kun, LIN Han-xing   

  1. School of Science, Tianjin University of Technology and Education, Tianjin 300222, China
  • Received:2016-03-07 Online:2016-06-20 Published:2016-06-15

PDF (PC)

1076

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

CLC Number: 

  • O154.2
[1] XI Changchang. Representation dimension and quasi-hereditary algebras[J]. Adv Math, 2002, 168:193-212.
[2] GUO Xiangqian. Representation dimension: An invaraint under stable equivalence[J]. Trans Amer Math Soc, 2005, 357:3255-3263.
[3] IYAMA O. Finiteness of representation dimension[J]. Proc Amer Math Soc, 2003, 131(4):1011-1014.
[4] ROUQUIER R. Representation dimension of exterior algebras[J]. Invent Math, 2006, 165(2):357-367.
[5] XI Changchang. On the representation dimension of finite dimensional algebras[J]. J Algebra, 2000, 226:332-346.
[6] COELHO F U, PLATZECK M I. On the representation dimension of some classes of algebras[J]. J Algebra, 2004, 275:615-628.
[7] OPPERMANN S. Wild algebras have one-point extensions of representation dimension at leasts four[J]. J Pure and Appl Algebra, 2009, 213(10):1945-1960.
[8] SAORIN M. Representation dimension of extensions of hereditary algebras[J]. J Pure and Appl Algebra, 2010, 214(9):1553-1558.
[9] ERDMANN K, HOLM T, IYAMA O, et al. Radical embeddings and representation dimension[J]. Adv Math, 2004, 185:159-177.
[10] ASSEM I. Tilting theory-an introduction, in: Topics in algebra[M] // Banach Centre Publ: vol.26, Warsaw, PWN, 1990: 127-180.
[1] LEI Xue-ping. Almost complete C-tilting modules [J]. J4, 2011, 46(2): 101-104.
[2] . AuslanderReiten correspondence for WCtilting modules [J]. J4, 2009, 44(12): 41-43.
[3] LEI Xue-ping . W-C-tilting modules [J]. J4, 2008, 43(10): 27-30 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd