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arXiv · 1609.08828

Geometry of mutation classes of rank $3$ quivers

Anna Felikson·Pavel Tumarkin
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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 $p^2+q^2+r^2-pqr$, where $p,q,r$ are the elements of exchange matrix. We also classify skew-symmetric mutation-finite real $3\times 3$ matrices and explore the structure of acyclic representatives in finite and infinite mutation classes.

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Anna Felikson, Pavel Tumarkin. 2017-06-15. Geometry of mutation classes of rank $3$ quivers. https://doi.org/10.1007/s40598-019-00101-2

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