On Derived Equivalences for Selfinjective Algebras
Authors:
Open Access
- 1 December 2006
- journal article
- research article
- Published by Taylor & Francis in Communications in Algebra
- Vol. 34 (12) , 4441-4452
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.Keywords
This publication has 17 references indexed in Scilit:
- Tilting complexes associated with a sequence of idempotentsJournal of Pure and Applied Algebra, 2003
- On t-structures and torsion theories induced by compact objectsJournal of Pure and Applied Algebra, 2002
- TILTING COMPLEXES DEFINED BY IDEMPOTENTSCommunications in Algebra, 2002
- ON DERIVED EQUIVALENT COHERENT RINGSCommunications in Algebra, 2002
- Representation Theory of Artin Algebras1995
- Piecewise Hereditary AlgebrasBulletin of the London Mathematical Society, 1988
- On splitting torsion theories induced by tilting modulesCommunications in Algebra, 1983
- Tilted algebrasTransactions of the American Mathematical Society, 1982
- Tilted algebras1981
- A torsion theory for Abelian categoriesTransactions of the American Mathematical Society, 1966