Modules of Gorenstein dimension zero over graph algebras

被引:1
作者
Golod, E. S. [1 ]
Pogudin, G. A. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia
关键词
Gorenstein dimension; CI-dimension; TOTALLY REFLEXIVE MODULES; LOCAL-RINGS; BRAUER-THRALL; CONSTRUCTION; CATEGORY; NUMBER;
D O I
10.1070/SM8563
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that nonfree modules of Gorenstein dimension zero over a graph algebra exist if and only if the graph is a tree. A classification of such modules is given.
引用
收藏
页码:964 / 982
页数:19
相关论文
共 19 条
  • [1] Avramov LL, 1998, PROG MATH, V166, P1
  • [2] Cohomology operators defined by a deformation
    Avramov, LL
    Sun, LC
    [J]. JOURNAL OF ALGEBRA, 1998, 204 (02) : 684 - 710
  • [3] AVRAMOV LL, 1997, PUBL MATH IHES, V86, P67
  • [4] Koszul duality patterns in representation theory
    Beilinson, A
    Ginzburg, V
    Soergel, W
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) : 473 - 527
  • [5] Brauer-Thrall for Totally Reflexive Modules over Local Rings of Higher Dimension
    Celikbas, Olgur
    Gheibi, Mohsen
    Takahashi, Ryo
    [J]. ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (03) : 997 - 1008
  • [6] CHRISTENSEN L. W., 2000, Lect. Notes in Math., V1747
  • [7] Brauer-Thrall for totally reflexive modules
    Christensen, Lars Winther
    Jorgensen, David A.
    Rahmati, Hamidreza
    Striuli, Janet
    Wiegand, Roger
    [J]. JOURNAL OF ALGEBRA, 2012, 350 (01) : 340 - 373
  • [8] Construction of totally reflexive modules from an exact pair of zero divisors
    Holm, Henrik
    [J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 : 278 - 288
  • [9] LOFWALL C, 1986, LECT NOTES MATH, V1183, P291
  • [10] A Construction of Totally Reflexive Modules
    Rahmati, Hamid
    Striuli, Janet
    Wiegand, Roger
    [J]. ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (01) : 103 - 111