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Piecewise Hereditary Nakayama Algebras

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Abstract

Let k be an algebraically closed field. Let Λ be the path algebra over k of the linearly oriented quiver \(\mathbb A_n\) for n ≥ 3. For r ≥ 2 and n > r we consider the finite dimensional k −algebra Λ(n,r) which is defined as the quotient algebra of Λ by the two sided ideal generated by all paths of length r. We will determine for which pairs (n,r) the algebra Λ(n,r) is piecewise hereditary, so the bounded derived category D b(Λ(n,r)) is equivalent to the bounded derived category of a hereditary abelian category \(\mathcal H\) as triangulated category.

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Dieter Happel

  2. Franz-Wolter-Str.33, 81925, Munich, Germany

    Uwe Seidel

Authors
  1. Dieter Happel
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  2. Uwe Seidel
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Correspondence to Dieter Happel.

Additional information

The results in this article are based on the doctoral thesis of the second author [19]. Some of the proofs have been modified and some recent developments have been taken into account. During a recent workshop in Bielefeld on the ADE Chain some interest was shown to make these results available to a wider audience.

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Happel, D., Seidel, U. Piecewise Hereditary Nakayama Algebras. Algebr Represent Theor 13, 693–704 (2010). https://doi.org/10.1007/s10468-009-9169-y

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  • DOI: https://doi.org/10.1007/s10468-009-9169-y

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