Dimensions of triangulated categories via Koszul objects
Petter Andreas Bergh, Srikanth B. Iyengar, Henning Krause, Steffen, Oppermann
TL;DR
This paper establishes lower bounds for the dimension of triangulated categories and applies these results to derive bounds on the representation dimensions of specific Artin algebras and complete intersection rings.
Contribution
It introduces new lower bounds for triangulated category dimensions and applies them to stable derived categories, advancing understanding of their structure and representation dimensions.
Findings
Lower bounds for triangulated category dimensions
Bounds for stable derived categories of Artin algebras
Bounds for representation dimensions of certain Artin algebras
Abstract
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra