An elementary construction of tilting complexes

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Let A be an artin algebra and e ε A an idempotent with add(eAA) = add(D(AAe)). Then a projective resolution of AeeAe gives rise to tilting complexes {P(l)•}1≥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 termlength l + 1. © 2002 Elsevier Science B.V. All rights reserved.




Hoshino, M., & Kato, Y. (2003). An elementary construction of tilting complexes. Journal of Pure and Applied Algebra, 177(2), 159–175.

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