On Derived Equivalences for Selfinjective Algebras |
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| Authors: | Hiroki Abe Mitsuo Hoshino |
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| Institution: | 1. Institute of Mathematics, University of Tsukuba , Ibaraki, Japan abeh@math.tsukuba.ac.jp;3. Institute of Mathematics, University of Tsukuba , Ibaraki, Japan |
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| Abstract: | We show that if A is a representation-finite selfinjective Artin algebra, then every P ? ? K b(𝒫 A ) with Hom K(Mod?A)(P ?,P ?i]) = 0 for i ≠ 0 and add(P ?) = add(νP ?) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B 0, B 1,…, B m = B such that, for any 0 ≤ i < m, B i+1 is the endomorphism algebra of a tilting complex for B i of length ≤ 1. |
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| Keywords: | Derived equivalence Selfinjective algebra Tilting complex Torsion theory |
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