Pentagon relation in quantum cluster scattering diagrams

2022/02/03 by Nakanishi, Tomoki
#13F60 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2202.01588

Abstract

We formulate the pentagon relation for quantum dilogarithm elements in the structure group of a quantum cluster scattering diagram (QCSD). As an application, we show the nonpositivity of a certain class of nonskew-symmetric QCSDs. Also, we explicitly present various consistency relations for QCSDs of rank 2 completely or up to some degree, many of which are new in the literature.

Related

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• Some coefficients of rank 2 cluster scattering diagrams
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• A Proof of the Pentagon Relation for Skeins
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