Tilting complexes associated with a sequence of idempotents

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Abstract

First, we show that a certain sequence of idempotents e0, e1,..., elin a ring A defines a tilting complex P•for A of term length l+1 and that there exists a sequence of rings B0=A,B1,..., Bl=EndK(Mod-A)(P•) such that for any 0≤i<l, Bi+1is the endomorphism ring of a tilting complex for Biof term length two defined by an idempotent. Next, in the case of A being a finite dimensional algebra over a field, we provide a construction of a two-sided tilting complex corresponding to P•. Simultaneously, we provide a sufficient condition for an algebra B containing A as a subalgebra to be derived equivalent to A. © 2003 Elsevier B.V. All rights reserved.

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Hoshino, M., & Kato, Y. (2003). Tilting complexes associated with a sequence of idempotents. Journal of Pure and Applied Algebra, 183(1–3), 105–124. https://doi.org/10.1016/S0022-4049(03)00012-4

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