Tilting-connected symmetric algebras

Preprint English OPEN
Aihara, Takuma;
(2010)
  • Subject: Mathematics - Rings and Algebras | Mathematics - Representation Theory
    arxiv: Mathematics::Category Theory

The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we give some sufficient conditions... View more
  • References (12)
    12 references, page 1 of 2

    [AH] H. Abe, M. Hoshino. On derived equivalences for selfinjective algebras, Comm. in Algebra 34 (2006), no. 12, 4441-4452.

    [A] T. Aihara. Mutating Brauer trees, arXiv: 1009.3210.

    [AI] T. Aihara, O. Iyama. Silting mutation in triangulated categories, arXiv: 1009.3370.

    [ASS] I. Assem, D. Simson, A. Skowronski. Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory, London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge, 2006.

    [B] K. Bongartz. Tilted algebras, Representations of algebras (Puebla, 1980), Lecture Notes in Math. Vol. 903. Springer, Berlin-New York, 1981, 26-38.

    [H] D. Happel. Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series, 119. Cambridge University Press, Cambridge, 1988.

    [HK] M. Hoshino, Y. Kato. Tilting complexes defined by idempotents, Comm. Algebra 30 (1), 83-100 (2002).

    [HS] B. Huisgen-Zimmermann, M. Saorin. Geometry of chain complexes and outer automorphisms under derived equivalence, Trans. Amer. Math. Soc., 353, 4757-4777, 2001.

    [O] T. Okuyama. Some examples of derived equivalent blocks of finite groups, preprint, 1998.

    [R1] J. Rickard. Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), 436-456.

  • Similar Research Results (1)
  • Metrics
    No metrics available
Share - Bookmark