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On Hochschild Cohomology for Selfinjective Special Biserial Algebras

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Book cover Algebras, Quivers and Representations

Part of the book series: Abel Symposia ((ABEL,volume 8))

Abstract

Let A be a selfinjective special biserial algebra. We introduce a short exact sequence of bimodules which gives new insight on the additive structure of the Hochschild cohomology.

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References

  1. M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995, xiv+423 pp.

    Book  MATH  Google Scholar 

  2. I. Assem, D. Simson, A. Skowroński, 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.

    Book  MATH  Google Scholar 

  3. R.-O. Buchweitz, E. L. Green, D. Madsen, Ø. Solberg, Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005) 805–816.

    MathSciNet  MATH  Google Scholar 

  4. M. C. R. Butler, A. D. King, Minimal resolutions of algebras, J. Algebra 212, no. 1 (1999), 323–362.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. C. R. Butler, C. M. Ringel, Auslander-Reiten sequences with few middle terms and applications to string algebras. Commun. Algebra 15, nos. 1–2 (1987), 145–179.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Erdmann, M. Holloway, N. Snashall, Ø. Solberg, R. Taillefer, Support varieties for selfinjective algebras, K-Theory 33, no. 1 (2004), 67–87.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Happel, Hochschild cohomology of finite-dimensional algebras, 108–126, Springer Lecture Notes in Mathematics 1404, 1989.

    Google Scholar 

  8. T. Holm, Hochschild cohomology of tame blocks, J. Algebra 271, no. 2 (2004), 798–826.

    Article  MathSciNet  MATH  Google Scholar 

  9. N. Snashall, A. E. Parker, A family of Koszul self-injective algebras with finite Hochschild cohomology, J. Pure Appl. Algebra 216, no. 5 (2012), 1245–1252.

    Article  MathSciNet  MATH  Google Scholar 

  10. N. Snashall, S. Schroll, Hochschild cohomology and support varieties for tame Hecke algebras. Q. J. Math. 62, no. 4 (2011), 1017–1029.

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. Lond. Math. Soc. 88 (2004), 705–732.

    Article  MathSciNet  MATH  Google Scholar 

  12. N. Snashall, R. Taillefer, The Hochschild cohomology ring of a class of special biserial algebras, J. Algebra Appl. 9, no. 1 (2010), 73–122.

    Article  MathSciNet  MATH  Google Scholar 

  13. Ø. Solberg, Support varieties for modules and complexes, Trends in representation theory of algebras and related topics, 239–270, Contemp. Math., 406, Am. Math. Soc., Providence, 2006.

    Chapter  Google Scholar 

  14. B. Wald, J. Waschbüsch, Tame biserial algebras, J. Algebra 95 (1985), 480–500.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Karin Erdmann .

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Erdmann, K. (2013). On Hochschild Cohomology for Selfinjective Special Biserial Algebras. In: Buan, A., Reiten, I., Solberg, Ø. (eds) Algebras, Quivers and Representations. Abel Symposia, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39485-0_4

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