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Stable Equivalence of Selfinjective Artin Algebras of Dynkin Type
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  • 作者:Andrzej Skowro艅ski (1)
    Kunio Yamagata (2)
  • 关键词:16D50 ; 16G10 ; 16G60 ; 16G70 ; 16S70 ; selfinjective algebra ; socle equivalence ; stable equivalence ; tilted algebra
  • 刊名:Algebras and Representation Theory
  • 出版年:2006
  • 出版时间:February 2006
  • 年:2006
  • 卷:9
  • 期:1
  • 页码:33-45
  • 全文大小:371KB
  • 参考文献:1. Assem, I. Happel, D. and Roldan, O.: Representation-finite trivial extension algebras, / J. Pure Appl. Algebra 33 (1984), 235鈥?42. CrossRef
    2. Assem, I. Nehring, J. and Skowro艅ski, A.; Domestic trivial extensions of simply connected algebras, / Tsukuba J. Math. 13 (1989), 31鈥?2.
    3. Assem, I. and Skowro艅ski, A.: Algebras with cycle-finite derived categories, / Math. Ann. 280 (1988), 441鈥?63. CrossRef
    4. Auslander, M. Reiten, I. and Smal酶, S. O.: / Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge University Press, 1995.
    5. Dlab, V. and Ringel, C. M.: Indecomposable representations of graphs and algebras, / Mem. Amer. Math. Soc. 173 (1976).
    6. Erdmann, K. Kerner, O. and Skowro艅ski, A.: Self-injective algebras of wild tilted type, / J. Pure Appl. Algebra 149 (2000), 127鈥?76. CrossRef
    7. Gabriel, P.: The universal cover of a representation-finite algebra, In: / Representations of Algebras, Lecture Notes in Math 903, Springer, New York, 1981, pp. 68鈥?05.
    8. Happel, D.: On the derived category of a finite-dimensional algebra, / Comment Math. Helv. 62 (1987), 339鈥?89. CrossRef
    9. Happel, D., Rickard, J. and Schofield, A.: Piecewise hereditary algebras, / Bull. London Math. Soc. 20 (1988), 23鈥?8. CrossRef
    10. Happel, D. and Ringel, C. M.: Tilted algebras, / Trans. Amer. Math. Soc. 274 (1982), 399鈥?43. CrossRef
    11. Hoshino, M.: Trivial extensions of tilted algebras, / Comm. Algebra 10 (1982), 1965鈥?999. CrossRef
    12. Hughes, D. and Waschb眉sch, J.: Trivial extensions of tilted algebras, / J. London Math. Soc. 46 (1983), 347鈥?64. CrossRef
    13. Martinez-Villa, R.: The stable equivalence for algebras of finite representation type, / Comm. Algebra 13 (1985), 991鈥?018. CrossRef
    14. Ohnuki, Y., Takeda, K. and Yamagata, K.: Automorphisms of repetitive algebras, / J. Algebra 232 (2000), 708鈥?24. CrossRef
    15. Peng, L. and Xiao, J.: Invariability of repetitive algebras of tilted algebras under stable equivalence, / J. Algebra 170 (1994), 54鈥?8. CrossRef
    16. Peng, L. and Xiao, J.: Invariability of trivial extensions of tilted algebras under stable equivalences, / J. London Math. Soc. 52 (1995), 61鈥?2.
    17. Reiten, I., Skowro艅ski, A. and Smal酶, S. O.: Short chains and regular components, / Proc. Amer. Math. Soc. 117 (1993), 601鈥?12. CrossRef
    18. Ringel, C. M.: / Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math 1099, Springer, New York, 1984.
    19. Skowro艅ski, A.: Selfinjective algebras of polynomial growth, / Math. Ann. 285 (1989), 177鈥?99. CrossRef
    20. Skowro艅ski, A.: Generalized standard Auslander鈥揜eiten components without oriented cycles, / Osaka J. Math. 30 (1993), 515鈥?27.
    21. Skowro艅ski, A.: Cycles in module categories, In: / Finite Dimensional Algebras and Related Topics, NATO ASI Series, Series C: Mathematical and Physical Sciences 424, Kluwer, Acad. Publ., Dordrecht, 1994, pp. 309鈥?45.
    22. Skowro艅ski, A. and Yamagata, K.: Socle deformations of self-injective algebras, / Proc. London Math. Soc. 72 (1996), 545鈥?66. CrossRef
    23. Skowro艅ski, A. and Yamagata, K.: Stable equivalence of selfinjective algebras of tilted type, / Arch. Math. (Basel) 70 (1998), 341鈥?50.
    24. Skowro艅ski, A. and Yamagata, K.: Galois coverings of selfinjective algebras by repetitive algebras, / Trans. Amer. Math. Soc. 351 (1999), 715鈥?34. CrossRef
    25. Skowro艅ski, A. and Yamagata, K.: On invariability of selfinjective algebras of tilted type under stable equivalences, / Proc. Amer. Math. Soc., 132 (2004), 659鈥?67. CrossRef
    26. Skowro艅ski, A. and Yamagata, K.: On selfinjective artin algebras having nonperiodic generalized standard Auslander鈥揜eiten components, / Colloq. Math., 96 (2003), 235鈥?44. CrossRef
    27. Tachikawa, H.: Representations of trivial extensions of hereditary algebras, In: / Representation Theory II, Lecture Notes in Math. 832, Springer, New York, 1980, pp. 579鈥?99.
    28. Tachikawa, H. and Wakamatsu, T.: Tilting functors and stable equivalences for selfinjective algebras, / J. Algebra 109 (1987), 138鈥?65. CrossRef
    29. Yamagata, K.: Extensions over hereditary Artinian rings with self-dualities I, / J. Algebra 73 (1981), 386鈥?33. CrossRef
    30. Yamagata, K.: Frobenius algebras, In: / Handbook of Algebra 1, Elsevier, Amsterdam, 1996, pp. 841鈥?87.
  • 作者单位:Andrzej Skowro艅ski (1)
    Kunio Yamagata (2)

    1. Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100, Toru艅, Poland
    2. Department of Mathematics, Tokyo University of Agriculture and Technology, Nakacho 2-24-16, Koganei, Tokyo, 184-8588, Japan
  • ISSN:1572-9079
文摘
We prove new results on the stable equivalences of selfinjective Artin algebras of tilted Dynkin type, extending the main results of Skowro艅ski and Yamagata to arbitrary tilted type.

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