Piecewise Hereditary Nakayama Algebras |
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Authors: | Dieter Happel Uwe Seidel |
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Institution: | 1.Fakult?t für Mathematik,Technische Universit?t Chemnitz,Chemnitz,Germany;2.Munich,Germany |
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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 An\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 H\mathcal H as triangulated category. |
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