Cluster tilting for one-dimensional hypersurface singularities

Advances in Mathematics - Tập 217 - Trang 2443-2484 - 2008
Igor Burban1, Osamu Iyama2, Bernhard Keller3, Idun Reiten4
1Johannes-Gutenberg Universität Mainz, Fachbereich Physik, Mathematik und Informatik, Institut für Mathematik, 55099 Mainz, Germany
2Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
3UFR de Mathématiques, UMR 7586 du CNRS, Case 7012, Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France
4Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet, N-7491 Trondheim, Norway

Tài liệu tham khảo

Amiot

Arnold, 1985, Singularities of Differentiable Maps, vol. I. The Classification of Critical Points, Caustics and Wave Fronts, vol. 82

Artin, 1977, Coverings of the rational double points in characteristic p, 11

Auslander, 1978, Functors and morphisms determined by objects, vol. 37, 1

Auslander, 1996, DTr-periodic modules and functors, vol. 18, 39

Białkowski, 2003, On tame weakly symmetric algebras having only periodic modules, Arch. Math., 81, 142, 10.1007/s00013-003-0816-y

Bondal, 1989, Representable functors, Serre functors and reconstructions, Izv. Akad. Nauk SSSR Ser. Mat., 53, 1183

Bongartz, 1983, Algebras and quadratic forms, J. London Math. Soc. (2), 28, 461, 10.1112/jlms/s2-28.3.461

Bongartz, 1981, Covering spaces in representation-theory, Invent. Math., 65, 331, 10.1007/BF01396624

Buan

Buan, 2006, Cluster-tilted algebras of finite representation type, J. Algebra, 306, 412, 10.1016/j.jalgebra.2006.08.005

Buan, 2007, Cluster-tilted algebras, Trans. Amer. Math. Soc., 359, 323, 10.1090/S0002-9947-06-03879-7

Buan, 2008, Cluster mutation via quiver representations, Comm. Math. Helv., 83, 10.4171/CMH/121

Buan, 2006, Tilting theory and cluster combinatorics, Adv. Math., 204, 572, 10.1016/j.aim.2005.06.003

Caldero, 2006, Quivers with relations arising from clusters (An case), Trans. Amer. Math. Soc., 358, 1347

Crawley-Boevey, 2000, On the exceptional fibre of Kleinian singularities, Amer. J. Math., 122, 1027, 10.1353/ajm.2000.0036

Dieterich, 1993, Lattices over curve singularities with large conductor, Invent. Math., 114, 399, 10.1007/BF01232675

Dieterich, 1986, Auslander–Reiten quiver of a simple curve singularity, Trans. Amer. Math. Soc., 294, 455, 10.1090/S0002-9947-1986-0825715-X

Drozd, 1993, Cohen–Macaulay module type, Compos. Math., 89, 315

Drozd, 2003, On Cohen–Macaulay modules on surface singularities, Mosc. Math. J., 3, 397, 10.17323/1609-4514-2003-3-2-397-418

Eisenbud, 1980, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc., 260, 35, 10.1090/S0002-9947-1980-0570778-7

Erdmann, 1990, Blocks of Tame Representation Type and Related Algebras, vol. 1428

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

Fomin, 2003

Geigle, 1987, A class of weighted projective curves arising in representation theory of finite-dimensional algebras, vol. 1273, 265

Geiss, 2006, Rigid modules over preprojective algebras, Invent. Math., 165, 589, 10.1007/s00222-006-0507-y

Greuel, 1985, Einfache Kurvensingularitäten und torsionsfreie Moduln, Math. Ann., 270, 417, 10.1007/BF01473437

Greuel, 2002

Greuel, 2006

Happel, 1988, Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, vol. 119

Happel

Happel, 1989, Almost complete tilting modules, Proc. Amer. Math. Soc., 107, 603, 10.1090/S0002-9939-1989-0984791-2

Happel, 2005, On a partial order of tilting modules, Algebr. Represent. Theory, 8, 147, 10.1007/s10468-005-3595-2

Holm, 1999, Derived equivalence classification of algebras of dihedral, semidihedral, and quaternion type, J. Algebra, 211, 159, 10.1006/jabr.1998.7544

Iyama, 2007, Higher-dimensional Auslander–Reiten theory on maximal orthogonal subcategories, Adv. Math., 210, 22, 10.1016/j.aim.2006.06.002

Iyama, 2007, Auslander correspondence, Adv. Math., 210, 51, 10.1016/j.aim.2006.06.003

Iyama

O. Iyama, Y. Yoshino, Mutation in triangulated categories and rigid Cohen–Macaulay modules, Invent. Math., in press

Kahn, 1989, Reflexive modules on minimally elliptic singularities, Math. Ann., 285, 141, 10.1007/BF01442678

Katz, 1991, Small resolutions of Gorenstein threefold singularities, vol. 116, 61

Keller, 2005, On triangulated orbit categories, Doc. Math., 10, 551, 10.4171/dm/199

Keller, 2007, Cluster-tilted algebras are Gorenstein and stably Calabi–Yau, Adv. Math., 211, 123, 10.1016/j.aim.2006.07.013

Knörrer, 1987, Cohen–Macaulay modules on hypersurface singularities I, Invent. Math., 88, 153, 10.1007/BF01405095

Koenig

Reid, 1983, Minimal models of canonical 3-folds, vol. 1, 131

Riedtmann, 1980, Algebren, Darstellungsköcher, Überlagerungen und zurück, Comment. Math. Helv., 55, 199, 10.1007/BF02566682

Riedtmann, 1991, On a simplicial complex associated with tilting modules, Comment. Math. Helv., 66, 70, 10.1007/BF02566636

Ringel, 1984, Tame Algebras and Integral Quadratic Forms, vol. 1099

Skowroński, 2006, Selfinjective algebras: Finite and tame type, vol. 406, 169

Solberg, 1989, Hypersurface singularities of finite Cohen–Macaulay type, Proc. London Math. Soc., 58, 258, 10.1112/plms/s3-58.2.258

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

Xiao, 2005, Locally finite triangulated categories, J. Algebra, 290, 473, 10.1016/j.jalgebra.2005.05.011

Yoshino, 1990, Cohen–Macaulay modules over Cohen–Macaulay rings, London Math. Soc. Lecture Note Ser., 146

Thông tin
Thông tin xuất bản

Advances in Mathematics

Tập 217

2443-2484

Thông tin tác giả