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Two-Term Partial Tilting Complexes Over Brauer Tree Algebras

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In this paper, all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 are described, using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an application, all two-term tilting complexes over a Brauer star algebra are described and their endomorphism rings are computed.

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References

  1. R. Rouquier and A. Zimmermann, “Picard groups for derived module categories,” Proc. London Math. Soc. (3), 87, No. 1, 197–225 (2003).

  2. I. Muchtadi-Alamsyah, “Braid action on derived category of Nakayama algebras,” Comm. Algebra, 36, No. 7, 2544–2569 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Abe and M. Hoshino, “On derived equivalences for self-injective algebras,” Comm. Algebra, 34, No. 12, 4441–4452 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Schaps and E. Zakay-Illouz, “Combinatorial partial tilting complexes for the Brauer star algebras,” in: Proceeding of the International Conference on Representations of Algebra, Sao Paulo (2001), pp. 187–208.

  5. M. Schaps and E. Zakay-Illouz, “Pointed Brauer trees,” J. Algebra, 246, No. 2, 647–672 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Rickard, “Morita theory for derived categories,” J. London Math. Soc., 39, No. 2, 436–456 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  7. I. M. Gelfand and V. A. Ponomarev, “Indecomposable representations of the Lorentz group,” Russian Math. Surv., 23, No. 2(140), 3–59 (1968).

  8. B. Wald and J. Waschbüsch, “Tame biserial algebras,” J. Algebra, 95, 480–500 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. A. Antipov and A. I. Generalov, “Finite generation of the Yoneda algebra of a symmetric special biserial algebra,” Algebra Analiz, 17, No. 3, 1–23 (2005).

    MathSciNet  Google Scholar 

  10. J. L. Alperin, Local Representation Theory, Cambridge Studies Adv. Math., 11, Cambridge University Press (1986).

  11. J. Rickard, “Derived categories and stable equivalence,” J. Pure Appl. Algebra, 61, 303–317 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Gabriel and C. Riedtmann, “Group representations without groups,” Comment. Math. Helv., 54, 240–287 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  13. M. C. R. Butler and C. M. Ringel, “Auslander–Reiten sequences with few middle terms and applications to string algebras,” Comm. Algebra, 15, Nos. 1–2, 145–179 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Happel, “Auslander–Reiten triangles in derived categories of finite-dimensional algebras,” Proc. Amer. Math. Soc., 112, 641–648 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Happel, Triangulated Categories in the Representation of Finite-Dimensional Algebras, Cambridge University Press (1988).

Download references

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Correspondence to M. A. Antipov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 413, 2013, pp. 5–25.

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Antipov, M.A., Zvonareva, A.O. Two-Term Partial Tilting Complexes Over Brauer Tree Algebras. J Math Sci 202, 333–345 (2014). https://doi.org/10.1007/s10958-014-2046-1

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  • DOI: https://doi.org/10.1007/s10958-014-2046-1

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