2011/09/28 by Jiaqun Wei, Wei, Jiaqun
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AC #math.CT #math.KT #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1109.6226
Comments are invited
arxiv created 2011/09/28 · arxiv updated 2011/09/29
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.