Auslander correspondence
Tài liệu tham khảo
Artin, 1986, Maximal orders of global dimension and Krull dimension two, Invent. Math., 84, 195, 10.1007/BF01388739
Artin, 1987, Graded algebras of global dimension 3, Adv. Math., 66, 171, 10.1016/0001-8708(87)90034-X
Assem, 2006, On the representation dimension of tilted and laura algebras, J. Algebra, 296, 426, 10.1016/j.jalgebra.2004.12.024
M. Auslander, Representation dimension of Artin algebras, in: Lecture Notes, Queen Mary College, London, 1971
Auslander, 1978, Functors and morphisms determined by objects, vol. 37, 1
Auslander, 1986, Isolated singularities and existence of almost split sequences, vol. 1178, 194
Auslander, 1986, Rational singularities and almost split sequences, Trans. Amer. Math. Soc., 293, 511, 10.1090/S0002-9947-1986-0816307-7
Auslander, 1989, The homological theory of maximal Cohen–Macaulay approximations, Mem. Soc. Math. Fr. (N.S.), 38, 5
Auslander, 1974, Stable equivalence of dualizing R-varieties, Adv. Math., 12, 306, 10.1016/S0001-8708(74)80007-1
Auslander, 1989, The Cohen–Macaulay type of Cohen–Macaulay rings, Adv. Math., 73, 1, 10.1016/0001-8708(89)90057-1
Auslander, 1991, Applications of contravariantly finite subcategories, Adv. Math., 86, 111, 10.1016/0001-8708(91)90037-8
Auslander, 1994, k-Gorenstein algebras and syzygy modules, J. Pure Appl. Algebra, 92, 1, 10.1016/0022-4049(94)90044-2
Auslander, 1996, D Tr-periodic modules and functors, vol. 18, 39
Auslander, 1972, A characterization of orders of finite lattice type, Invent. Math., 17, 79, 10.1007/BF01390025
Auslander, 1981, Almost split sequences in subcategories, J. Algebra, 69, 426, 10.1016/0021-8693(81)90214-3
Auslander, 1993, Gorenstein algebras and algebras with dominant dimension at least 2, Comm. Algebra, 21, 3897, 10.1080/00927879308824773
Auslander, 1995, Representation Theory of Artin Algebras, vol. 36
Bjork, 1989, The Auslander condition on Noetherian rings, vol. 1404, 137
Bocian, 2004, The representation dimension of domestic weakly symmetric algebras, Cent. Eur. J. Math., 2, 67, 10.2478/BF02475951
Bondal
Buan, 2006, Tilting theory and cluster combinatorics, Adv. Math., 204, 572, 10.1016/j.aim.2005.06.003
Clark, 2001, Auslander–Gorenstein rings for beginners, 95
Coelho, 2004, On the representation dimension of some classes of algebras, J. Algebra, 275, 615, 10.1016/j.jalgebra.2003.09.022
Curtis, 1990, Methods of Representation Theory, vol. I. With Applications to Finite Groups and Orders
A. Dugas, Representation dimension as a relative homological invariant of stable equivalence, Algebr. Represent. Theory, in press
Erdmann, 2004, Radical embeddings and representation dimension, Adv. Math., 185, 159, 10.1016/S0001-8708(03)00169-5
Fomin, 2002, Cluster algebras. I. Foundations, J. Amer. Math. Soc., 15, 497, 10.1090/S0894-0347-01-00385-X
Fomin, 2003, Cluster algebras. II. Finite type classification, Invent. Math., 154, 63, 10.1007/s00222-003-0302-y
Fossum, 1975, Trivial extensions of abelian categories, vol. 456
Geiss, 2005, Extension-orthogonal components of preprojective varieties, Trans. Amer. Math. Soc., 357, 1953, 10.1090/S0002-9947-04-03555-X
Geiss, 2005, Semicanonical bases and preprojective algebras, Ann. Sci. École Norm. Sup. (4), 38, 193, 10.1016/j.ansens.2004.12.001
C. Geiss, B. Leclerc, J. Schröer, Rigid modules over preprojective algebras, Invent. Math., in press
Goto, 1999, Minimal injective resolutions of Cohen–Macaulay isolated singularities, Arch. Math. (Basel), 73, 249, 10.1007/s000130050394
Goto, 2002, Towards a theory of Bass numbers with application to Gorenstein algebras, Colloq. Math., 91, 191, 10.4064/cm91-2-4
Guo, 2005, Representation dimension: An invariant under stable equivalence, Trans. Amer. Math. Soc., 357, 3255, 10.1090/S0002-9947-04-03596-2
Happel, 1988, Triangulated Categories in the Representation Theory of Finite-dimensional Algebras, vol. 119
Hoshino, 1989, On dominant dimension of Noetherian rings, Osaka J. Math., 26, 275
Holm, 2003, Representation dimension of some tame blocks of finite groups, Algebra Colloq., 10, 275
Iyama, 2003, Finiteness of representation dimension, Proc. Amer. Math. Soc., 131, 1011, 10.1090/S0002-9939-02-06616-9
Iyama, 2003, Symmetry and duality on n-Gorenstein rings, J. Algebra, 269, 528, 10.1016/S0021-8693(03)00419-8
Iyama, 2004, Representation dimension and Solomon zeta function, vol. 40, 45
Iyama, 2005, τ-Categories III: Auslander orders and Auslander–Reiten quivers, Algebr. Represent. Theory, 8, 601, 10.1007/s10468-005-0970-y
Iyama, 2005, The relationship between homological properties and representation theoretic realization of Artin algebras, Trans. Amer. Math. Soc., 357, 709, 10.1090/S0002-9947-04-03482-8
Iyama
Iyama, 2007, Higher dimensional Auslander–Reiten theory on maximal orthogonal subcategories, Adv. Math., 210, 22, 10.1016/j.aim.2006.06.002
Igusa, 2005, On the finitistic global dimension conjecture for Artin algebras, vol. 45, 201
Krause
G. Leuschke, Endomorphism rings of finite global dimension, Canad. J. Math., in press
Matsumura, 1989, Commutative Ring Theory, vol. 8
McKay, 1980, Graphs, singularities, and finite groups, vol. 37, 183
Miyachi, 2000, Injective resolutions of Noetherian rings and cogenerators, Proc. Amer. Math. Soc., 128, 2233, 10.1090/S0002-9939-00-05305-3
Miyashita, 1986, Tilting modules of finite projective dimension, Math. Z., 193, 113, 10.1007/BF01163359
Nishida, 2006, Cohen–Macaulay isolated singularities with a dualizing module, Algebr. Represent. Theory, 9, 13, 10.1007/s10468-005-9004-z
de la Pena, 1991, On the dimension of the module-varieties of tame and wild algebras, Comm. Algebra, 19, 1795, 10.1080/00927879108824229
Ramras, 1969, Maximal orders over regular local rings of dimension two, Trans. Amer. Math. Soc., 142, 457, 10.1090/S0002-9947-1969-0245572-2
Reiten, 1989, Two-dimensional tame and maximal orders of finite representation type, Mem. Amer. Math. Soc., 80
Riedtmann, 1980, Algebren, Darstellungskocher, Überlagerungen und zurück, Comment. Math. Helv., 55, 199, 10.1007/BF02566682
Rouquier, 2006, Representation dimension of exterior algebras, Invent. Math., 165, 357, 10.1007/s00222-006-0499-7
Rouquier
Tachikawa, 1973, Quasi-Frobenius Rings and Generalizations, vol. 351
Van den Bergh, 2004, Three-dimensional flops and noncommutative rings, Duke Math. J., 122, 423, 10.1215/S0012-7094-04-12231-6
Van den Bergh, 2004, Non-commutative crepant resolutions, 749
Xi, 2002, Representation dimension and quasi-hereditary algebras, Adv. Math., 168, 193, 10.1006/aima.2001.2046
Yoshino, 1990, Cohen–Macaulay modules over Cohen–Macaulay rings, vol. 146