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关于有限维数猜想的一些新进展 被引量：3

Some New Advances in Finitistic Dimension Conjecture
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摘要 在Artin代数的表示理论中,有一个著名的有限维数猜想：任意给定一个Artin代数,它的有限维数都是有限的．这个猜想已有45年的历史,至今悬而未决．本文主要综述它的一些历史发展情况,并介绍关于有限维数猜想的一些最新进展． In the representation theory of Artin algebras, there is a well-known conjecture： Given an arbitrary Artin algebra, its finitistic dimension is finite. This is called the finitistic dimension conjecture. It is over 45 years old and remains open to date. In this note, We survey its developments, and report some of the new advances on the finitistic dimension conjecture.
作者 惠昌常
机构地区 北京师范大学数学科学学院
出处 《数学进展》 CSCD 北大核心 2007年第1期13-17,共5页 Advances in Mathematics（China）
基金 教育部高校博士点基金(No.0040027002)和CFKSTIP(No.704004)
关键词 ARTIN代数 JACOBSON根 投射维数 表示维数 有限维数 Artin algebra syzygy of module projective dimension representation dimension finitistic dimension.
分类号 O153.3 [理学—基础数学] O154.1 [理学—基础数学]
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参考文献31

  • 1Agoston,I.,Happel,D.,Lukacs,E.and Unger,L.,Finitistic dimension of standardly stratified algebras,Comm.Algebra,2000,28(6):2745-2752.
  • 2Auslander,M.,Representation Dimension of Artin Algebras,Queen Mary College Mathematics Notes,Queen Mary College,London,1971.
  • 3Auslander,M.and Reiten,I.,On a generalized version of the Nakayama conjecture,Proc.Amer.Math.Soc,1975,52:69-74.
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同被引文献42

  • 1Asashiba, H., On a lift of an individual stable equivalence to a standard derived equivalence for representation- finite self-injective algebras, Algebras and Representation Theory, 2003, 6(4): 427-447.
  • 2Auslander, M., Representation Dimension of Artin Algebras, Queen Mary College Mathematics Notes, Queen Mary College, London, 1971.
  • 3Anderson, F.W. and Fuller, K.R., Rings and Categories of Modules, Graduate Texts in Math. 13, 1973.
  • 4Auslander, M. and Platzeck, I., Representation theory of hereditary artin algerbas, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York and Basel, 1978, 37: 389-424.
  • 5Auslander, M. and Reiten, I., Stable equivalence of Artin algebras, Proceedings of the Conference on Orders, groups and related topics, Lecture Notes in Math., 1973, 353: 8-71.
  • 6Auslander, M. and Reiten, I., Stable equivalence of dualizing R-varieties I, Adv. Math., 1974, 12: 306-366.
  • 7Auslander, M., Reiten, I. and Smalφ, S., Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, 1995.
  • 8Beligannis, A., Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras, J. Algebra, 2005, 288: 137-211.
  • 9Broue, M., On Representations of Symmetric Algebras: An Introduction, Course Notes by M. Stricker, Forschungsinstitut fur Mathematik der ETH Zurich, 1991.
  • 10Broue, M., Equivalences of Blocks of Group Algebras, Finite Dimensional Algebras and Related Topics, V. Dlab and L. L. Scott(eds.), Kluwer, 1994: 1-26.

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数学进展
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