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d-Cluster范畴的Grothendieck群 被引量：3

Grothendieck groups of d-Cluster categories
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摘要 2008年,Barot,Kussin,Lenzing对代数闭域上的有限表示型的遗传代数的Cluster范畴的Grothendieck群做了刻画.作者在本文中对其推广,得到了代数闭域上有限表示型遗传代数上的d-Cluster范畴的Grothendieck群. In 2008, Barot, Kussin, Lenzing described the Grothendieck groups of Cluster categories of hereditary algebras of finite representation type. In this paper, the authors get a more widely result. They describe the Grothendieek groups of d-Cluster categories of hereditary algebras of finite representa- tion type.
作者 马洪芹 耿圣飞
机构地区 四川大学数学学院
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第2期299-302,共4页 Journal of Sichuan University(Natural Science Edition)
关键词 GROTHENDIECK群 d—Cluster范畴 Cluster范畴 Grothendieck groups, d-Cluster categories, Cluster categories
分类号 O152.6 [理学—基础数学]
  • 相关文献

参考文献12

  • 1Fomin S, Zelevinsky A. Cluster algebra I : Foundations [J]. J Amer Math Soe, 2002, 15,(2): 497.
  • 2Fomin S, Zelevinsky A. Cluster algebra Ⅱ : Finitetype classification [J]. Invent Math, 2003, 154: 63.
  • 3Buan A, Marsh R, Reineke M. Tilting theory and cluster combinatorics [J]. Adv Math, 2006, 204: 572.
  • 4Buan A, Marsh R. Cluster-tilting theory [C] // Peria J I, Bautista R. Trends in Representation Theory of Algebras and Related Topics. Providence, RI:Amer Math Soc, 2006.1.
  • 5Rieten I. Tilting theory and cluster algebras [J]. Preprint,.
  • 6RingeI M C. Some remarks concerning tilting mod-ules and tilted algebras. Origin. Relevance. Future. An appendix to the Handbook of tilting theory,edited by Lidia Angeleri-Hugel, Dieter Happel and Henning Krause [ M ]. Cambridge: Cambridge University Press, 2007.
  • 7邹腾.图的循环定向[J].四川大学学报（自然科学版）,2010,47(1):21-26. 被引量：1
  • 8Keller B. Triangulated orbit categories [J]. Documenta Math, 2005, 10: 551.
  • 9Barot M, Kussin D, Lenzing H. The grothendieck group of a cluster category[J]. J Pure Applied Algebra, 2008, 212: 33.
  • 10Hanppel D. Triangulated categories in the representation theory of finite dimensional algebras IMP. Cambridge: Cambridge University Press, 1988.

二级参考文献13

  • 1Fomin S, Zelevinsky A. Cluster algebras I. foundations [J]. Amer Math Soc, 2002(2): 497.
  • 2Fomin S, Zelevinsky A. Double Bruhat cells and total positivity [J]. Amer Math Soc, 1999(12) : 335.
  • 3Lusztig G. Introduction to total positivity[C]//Posivity in Lie theory: open problems. Berlin.. de Gruyter, 1998.
  • 4Buan A B, Marsh R, Reineke M, Et A L. Tilting theory and cluster combinatorics [J]. Adv Math, 2004(1) : 1.
  • 5Marsh R, Reineke M, Zelevinsky A. Generallized assoeiahedra via quiver representation [J]. Tran Amer Math Soc, 2003(10) : 4171.
  • 6Barot M, Geiss C, Zelevinsky A. Cluster algebras of finite type and positive symmetrizable matrices [J]. London Math Soc, 2006(3) : 545.
  • 7Hartshome R. Residue and duality [ M]. Berlin/New York: Springer, 1966.
  • 8Iversen B. Cohomology of sheaves[M]. New York/ Berlin: Springer-Verlag, 1986.
  • 9Beilinson A A, Bernstein J, Deligne P. Faisceaux pervers[J]. Asterisque, 1982, 100: 1.
  • 10Verdier J L. Categories derivees[M], Berlin/New York: Springer, 1977.

共引文献2

同被引文献50

  • 1Verdier J L. Categories d6riv6es [M]. Berlin: Springer, 1977.
  • 2Happel D. Triangulated categories in the representa- tion theory of finite-dimensional algebras[M]. Lon- don: Cambridge University Press, 1988.
  • 3Keller B. On triangulated orbit categories[J]. Doc Math, 2005, 10: 551.
  • 4Buan A B, Marsh R J, Reineke M, et al. Tilting the- ory and cluster eombinatorics[J]. Adv Math, 2006, 204: 572.
  • 5Xiao j, Zhu B. Locally finite triangulated categories [J].J Algebra, 2005, 290: 473.
  • 6Amiot C. On the structure of triangulated categories with finitely many indeeomposables[EB/OL], arXiv: math/0612141v2 [math. CT]12 Jan 2007.
  • 7Peng L G. Conical extensions of derived categories [R]. Torufi: XII International Conference on Repre- sentations of Algebras and Workshop, 2007.
  • 8Weibel C A. An introduction to homological algebra [M]. Beijing: China Machine Press, 2004.
  • 9Auslander M, Reiten I, Smal~S O. Representation theory of artin algeras [M]. London: Cambrige University Press, 1995.
  • 10Cartan H, Eilenberg S. Homological algebra[M]. Princeton: Princeton University Press, 1956.

引证文献3

二级引证文献2

四川大学学报（自然科学版）
2011年 第2期

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