An elementary construction of tilting complexes

https://doi.org/10.1016/S0022-4049(02)00176-7Get rights and content
Under an Elsevier user license
open archive

Abstract

Let A be an artin algebra and eA an idempotent with add(eAA)=add(D(AAe)). Then a projective resolution of AeeAe gives rise to tilting complexes {P(l)}l⩾1 for A, where P(l) is of term length l+1. In particular, if A is self-injective, then EndK(Mod-A)(P(l)) is self-injective and has the same Nakayama permutation as A. In case A is a finite dimensional algebra over a field and eAe is a Nakayama algebra, a projective resolution of eAe over the enveloping algebra of eAe gives rise to two-sided tilting complexes {T(2l)}l⩾1 for A, where T(2l) is of term length 2l+1. In particular, if eAe is of Loewy length two, then we get tilting complexes {T(l)}l⩾1 for A, where T(l) is of term length l+1.

MSC

Primary: 18E30
16G30
secondary: 18E35
16E05

Cited by (0)