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Journal of Mathematical Sciences

, Volume 209, Issue 4, pp 568–587 | Cite as

Two-Term Tilting Complexes over Brauer Tree Algebras

  • A. O. Zvonareva
Article

In this paper, all two-term tilting complexes over a Brauer tree algebra with multiplicity one are described, using a classification of indecomposable two-term partial tilting complexes obtained earlier in a joint paper with M. Antipov. The endomorphism rings of such complexes are computed.

Keywords

Nonzero Component Projective Module Endomorphism Ring Triangulate Category Marked Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Rouquier and A. Zimmermann, “Picard groups for derived module categories,” Proc. London Math. Soc., (3) 87, No. 1, 197–225 (2003).Google Scholar
  2. 2.
    I. Muchtadi-Alamsyah, “Braid action on derived category of Nakayama algebras,” Comm. Algebra, 36, No. 7, 2544–2569 (2008).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    M. Schaps and E. Zakay-Illouz, “Braid group action on the refolded tilting complex of the Brauer star algebra,” Proceedings ICRA IX (Beijing), 2, 434–449 (2002).MathSciNetGoogle Scholar
  4. 4.
    H. Abe and M. Hoshino, “On derived equivalences for selfinjective algebras,” Comm. Algebra, 34, No. 12, 4441–4452 (2006).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    T. Adachi, O. Iyama, and I. Reiten, “τ -tilting theory,” to appear in Compos. Math., arXiv:1210.1036, (2012).Google Scholar
  6. 6.
    A. Chan, “Two-term tilting complexes of Brauer star algebra and simple-minded systems,” arXiv:1304.5223, (2013).Google Scholar
  7. 7.
    M. Antipov and A. Zvonareva. “Two-term partial tilting complexes over Brauer tree algebras. Problems in the theory of representations of algebras and groups,” Zap. Nauchn. Semin. POMI, 413, 5–25 (2013).MathSciNetGoogle Scholar
  8. 8.
    I. M. Gelfand and V. A. Ponomarev, “Indecomposable representations of the Lorentz group,” Russian Math. Surveys, 23, No. 2 (140), 3–59 (1968).MathSciNetGoogle Scholar
  9. 9.
    B. Wald and J. Waschbüsch, “Tame biserial algebras,” J. Algebra, 95, 480–500 (1985).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    J. Rickard, “Derived categories and stable equivalence,” J. Pure Appl. Algebra, 61, 303–317 (1989).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    P. Gabriel and C. Riedtmann, “Group representations without groups,” Comment. Math. Helv., 54, 240–287 (1979).MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    D. Happel, “Auslander-Reiten triangles in derived categories of finite-dimensional algebras,” Proc. Amer. Math. Soc., 112, 641–648 (1991).MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    D. Happel, “Triangulated Categories in the Representation of Finite Dimensional Algebras,” Cambridge Univ. Press (1988).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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