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Tame triangular matrix algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra $T_2(A)$ of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which $T_2(A)$ is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
Słowa kluczowe
Rocznik
Tom
86
Numer
2
Strony
259-303
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-03-29
poprawiono
2000-04-28
Twórcy
  • Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. 56 1988 417-450
  • [2] M. Auslander, M. I. Platzeck and I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 1979 1-46
  • [3] M. Auslander and I. Reiten, On the representation type of triangular matrix rings, J. London Math. Soc. 12 1976 371-382
  • [4] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1985.
  • [5] R. Bautista, P. Gabriel, A. V. Roiter and L. Salmerón, Representation-finite algebras and multiplicative bases, Invent. Math. 81 1985 217-285
  • [6] K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. 28 1983 461-469
  • [7] K. Bongartz, Critical simply connected algebras, Manuscripta Math. 46 1984 117-136
  • [8] K. Bongartz, A criterion for finite representation type, Math. Ann. 269 1984 1-12
  • [9] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 69 1981 331-378
  • [10] S. Brenner, Large indecomposable modules over a ring of 2×2 triangular matrices, Bull. London Math. Soc. 3 1971 333-336
  • [11] S. Brenner, On two questions of M. Auslander, ibid. 4 1972 301-302
  • [12] O. Bretscher and P. Gabriel, The standard form of a representation-finite algebra, Bull. Soc. Math. France 111 1983 21-40
  • [13] W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 1988 451-483
  • [14] W. W. Crawley-Boevey, Tame algebras and generic modules, ibid. 63 1991 241-265
  • [15] P. Dowbor and A. Skowroński, On Galois coverings of tame algebras, Arch. Math. (Basel) 44 1985 522-529
  • [16] P. Dowbor and A. Skowroński, On the representation type of locally bounded categories, Tsukuba J. Math. 10 1986 63-77
  • [17] P. Dowbor and A. Skowroński, Galois coverings of representation-infinite algebras, Comment. Math. Helv. 62 1987 311-337
  • [18] P. Dräxler and A. Skowroński, Biextensions by indecomposable modules of derived regular length 2, Compositio Math. 117 1999 205-221
  • [19] Yu. A. Drozd, Tame and wild matrix problems, in: Representation Theory II, Lecture Notes in Math. 832, Springer, 1980, 242-258
  • [20] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Representation Theory I, Lecture Notes in Math. 831, Springer, 1980, 1-71
  • [21] P. Gabriel, The universal cover of a representation-finite algebra, in: Representations of Algebras, Lecture Notes in Math. 903, Springer, 1981, 68-105
  • [22] D. Happel and D. Vossieck, Minimal algebras of finite representation type with preprojective component, Manuscripta Math. 42 1983 221-243
  • [23] M. Hishino and I. Miyachi, Tame triangular matrix algebras over self-injective algebras, Tsukuba J. Math. 11 1987 383-391
  • [24] K. Igusa, M. I. Platzeck, G. Todorov and D. Zacharia, Auslander algebras of finite representation type, Comm. Algebra 15 1987 377-424
  • [25] O. Kerner, Tilting wild algebras, J. London Math. Soc. 39 1989 29-47
  • [26] O. Kerner and A. Skowroński, On module categories with nilpotent infinite radical, Compositio Math. 77 1991 313-333
  • [27] M. Lersch, Minimal wilde Algebren, Diplomarbeit, Düsseldorf, 1987.
  • [28] Z. Leszczyński, l-hereditary triangular matrix algebras of tame representation type, Arch. Math. (Basel) 54 1990 25-31
  • [29] Z. Leszczyński, On the representation type of triangular matrix algebras over special algebras, Fund. Math. 137 1991 65-80
  • [30] Z. Leszczyński, On the representation type of tensor product algebras, ibid. 144 1994 143-161
  • [31] Z. Leszczyński and D. Simson, On the triangular matrix rings of finite type, J. London Math. Soc. 20 1979 386-402
  • [32] Z. Leszczyński and A. Skowroński, Auslander algebras of tame representation type, in: Representation Theory of Algebras, CMS Conf. Proc. 18, Amer. Math. Soc., 1986, 475-486
  • [33] N. Marmaridis, On the representation type of certain triangular matrix rings, Comm. Algebra 11 1983 1945-1964
  • [34] R. Nörenberg and A. Skowroński, Tame minimal non-polynomial growth simply connected algebras, Colloq. Math. 73 1997 301-330
  • [35] J. A. de la Peña, Algebras with hypercritical Tits form, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa, 1990, 353-369
  • [36] J. A. de la Peña, On the dimension of the module-varieties of tame and wild algebras, Comm. Algebra 19 1991 1795-1807
  • [37] C. M. Ringel, Tame algebras, in: Representation Theory I, Lecture Notes in Math. 831, Springer, 1980, 137-287
  • [38] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
  • [39] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, 1992.
  • [40] A. Skowroński, Tame triangular matrix algebras over Nakayama algebras, J. London Math. Soc. 34 1986 245-264
  • [41] A. Skowroński, On tame triangular matrix algebras, Bull. Polish Acad. Sci. Math. 34 1986 517-523
  • [42] A. Skowroński, Group algebras of polynomial growth, Manuscripta Math. 59 1987 499-516
  • [43] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa, 1990, 535-468
  • [44] A. Skowroński, Simply connected algebras and Hochschild cohomologies, in: Representations of Algebras, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 431-447
  • [45] A. Skowroński, Module categories over tame algebras, in: Representation Theory and Related Topics, CMS Conf. Proc. 19, Amer. Math. Soc., 1996, 281-313
  • [46] A. Skowroński, Simply connected algebras of polynomial growth, Compositio Math. 109 1997 99-133
  • [47] A. Skowroński, Tame algebras with strongly simply connected Galois coverings, Colloq. Math. 72 1997 335-351
  • [48] L. Unger, The concealed algebras of the minimal wild hereditary algebras, Bayreuth. Math. Schr. 31 1990 145-154
  • [49] J. Wittmann, Verkleidete zahne und minimal Algebren, Diplomarbeit, Bayreuth, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv86i2p259bwm
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