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arXiv · 1904.03928

Exchange graphs for mutation-finite non-integer quivers of rank 3

Anna Felikson·Philipp Lampe
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Abstract

Skew-symmetric non-integer matrices with real entries can be viewed as quivers with non-integer weights of arrows. One can mutate such quivers according to usual rules of quiver mutation. Felikson and Tumarkin show that rank 3 mutation-finite non-integer quivers admit geometric realisations by partial reflections. This allows to define a notion of seeds (as Y-seeds), and hence, to define the exchange graphs for mutation classes. In this paper we study exchange graphs of mutation-finite quivers in rank 3. The concept of finite and affine type generalises naturally to non-integer quivers. In particular, exchange graphs of finite type quivers are finite, while exchange graphs of affine quivers are finite modulo the action of a finite-dimensional lattice.

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Anna Felikson, Philipp Lampe. 2019-04-08. Exchange graphs for mutation-finite non-integer quivers of rank 3. https://arxiv.org/abs/1904.03928

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