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Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r

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arxiv 1001.1880 v4 pith:URVD4OAJ submitted 2010-01-12 math.QA math.RT

Rei Inoue , Osamu Iyama , Bernhard Keller , Atsuo Kuniba , Tomoki Nakanishi This is my paper · ORCID
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keywords y-systemsassociatedperiodicitiestypealgebraclusterdilogarithmidentities
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We prove the periodicities of the restricted T and Y-systems associated with the quantum affine algebra of type B_r at any level. We also prove the dilogarithm identities for the Y-systems of type B_r at any level. Our proof is based on the tropical Y-systems and the categorification of the cluster algebra associated with any skew-symmetric matrix by Plamondon. Using this new method, we also give an alternative and simplified proof of the periodicities of the T and Y-systems associated with pairs of simply laced Dynkin diagrams.

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  1. Half-periodicity of Zamolodchikov periodic cluster algebras

    math.CO 2026-02 conditional novelty 6.0 of 10

    For every Zamolodchikov periodic cluster algebra, the T-system at half the period is a permutation of order at most two of the initial cluster variables.

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