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.
2000 Mathematics Subject Classification:
Notes
Communicated by D. Happel.