Baur, K orcid.org/0000-0002-7665-476X and Marsh, RJ orcid.org/0000-0002-4268-8937 (2012) A geometric model of tube categories. Journal of Algebra, 362. pp. 178-191. ISSN 0021-8693
Abstract
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between corresponding arcs, giving a geometric interpretation of the description of an extension group in the cluster category of a tube as a symmetrized version of the extension group in the tube. We show that a similar result holds for finite dimensional representations of the linearly oriented quiver of type A.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: | |
Keywords: | primary; 16G10; 16G20; 16G70; 18E30; 14C17; secondary; 13F60 |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/G007497/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Aug 2019 15:28 |
Last Modified: | 22 Aug 2019 15:28 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jalgebra.2012.04.009 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149692 |