Professor Anna Felikson anna.felikson@durham.ac.uk
Professor
Geometry of mutation classes of rank 3 quivers
Felikson, A.; Tumarkin, P.
Authors
Professor Pavel Tumarkin pavel.tumarkin@durham.ac.uk
Professor
Abstract
We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by π-rotations for the cyclic ones. The geometric behavior of the model turns out to be controlled by the Markov constant p2 + q2 + r 2 − pqr, where p, q,r are the weights of arrows in a quiver. We also classify skew-symmetric mutation-finite real 3×3 matrices and explore the structure of acyclic representatives in finite and infinite mutation classes.
Citation
Felikson, A., & Tumarkin, P. (2019). Geometry of mutation classes of rank 3 quivers. Arnold Mathematical Journal, 5(1), 37-55. https://doi.org/10.1007/s40598-019-00101-2
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 18, 2019 |
Online Publication Date | Mar 4, 2019 |
Publication Date | Mar 31, 2019 |
Deposit Date | Oct 27, 2016 |
Publicly Available Date | Mar 28, 2024 |
Journal | Arnold Mathematical Journal |
Print ISSN | 2199-6792 |
Electronic ISSN | 2199-6806 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 5 |
Issue | 1 |
Pages | 37-55 |
DOI | https://doi.org/10.1007/s40598-019-00101-2 |
Related Public URLs | http://arxiv.org/abs/1609.08828 |
Files
Published Journal Article (Advance online version)
(514 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
Advance online version © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Published Journal Article
(503 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
You might also like
Exhange graphs for mutation-finite non-integer quivers
(2023)
Journal Article
Cluster algebras of finite mutation type with coefficients
(2023)
Journal Article
Mutation-finite quivers with real weights
(2023)
Journal Article
Friezes for a pair of pants
(2022)
Journal Article
Cluster algebras from surfaces and extended affine Weyl groups
(2021)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search