Tilting complexes associated with a sequence of idempotents
- Hoshino, Mitsuo
- Kato, Yoshiaki
Publication date
September 2003
DOI Publisher
Elsevier B.V. ISSN
0022-4049Abstract
AbstractFirst, we show that a certain sequence of idempotents e0,e1,…,el in 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+1 is the endomorphism ring of a tilting complex for Bi of 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
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