Derived categories and syzygies

Details Derived categories and syzygies Derived categories and syzygies

2011-09-28

arxiv.org/abs/1109.6226v1

Mathematics

Representation Theory

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Scientific paper

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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