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arXiv · 1812.00871

Quantum dilogarithm identities for n-cycle quivers

Justin Allman
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Abstract

We prove quantum dilogarithm identities for $n$-cycle quivers. By the combinatorial approach of Keller, each side of our identity determines a maximal green sequence of quiver mutations. Thus we interpret our identities as factorizations of the refined Donaldson--Thomas invariant for the quiver with potential. Finally, we conjecture an upper bound on the possible lengths of maximal green sequences.

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Justin Allman. 2018-12-03. Quantum dilogarithm identities for n-cycle quivers. https://arxiv.org/abs/1812.00871

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