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Geometry of mutation classes of rank 3 quivers.

Felikson, A. and Tumarkin, P. (2019) 'Geometry of mutation classes of rank 3 quivers.', Arnold mathematical journal., 5 (1). pp. 37-55.

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.

Item Type:Article
Full text:Publisher-imposed embargo
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s40598-019-00101-2
Publisher statement:© 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.
Date accepted:18 February 2019
Date deposited:19 February 2019
Date of first online publication:04 March 2019
Date first made open access:No date available

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