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Derived categories and syzygies

Published 28 Sep 2011 in math.RT, math.AC, math.CT, math.KT, and math.RA | (1109.6226v1)

Abstract: We introduce syzygies for derived categories and study their properties. Using these, we prove the derived invariance of the following classes of artin algebras: (1) syzygy-finite algebras, (2) Igusa-Todorov algebras, (3) AC algebras, (4) algebras satisfying the finitistic Auslander conjecture, and (5) algebras satisfying the generalized Auslander-Reiten conjecture. In particular, Gorenstein CM-finite algebras are derived invariants.

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