An elementary construction of tilting complexes

✍ Scribed by Mitsuo Hoshino; Yoshiaki Kato

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 189 KB
• Volume: 177
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00176-7

✦ Synopsis

Let A be an artin algebra and e ∈ A 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 End K(Mod-A) (P(l) • ) is self-injective and has the same Nakayama permutation as A. In case A is a ÿnite dimensional algebra over a ÿeld 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.