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On cluster theory and quantum dilogarithm identities

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arxiv 1102.4148 v4 pith:DCZD4KWZ submitted 2011-02-21 math.RT math.COmath.QA

Bernhard Keller This is my paper · ORCID
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These are expanded notes from three survey lectures given at the 14th International Conference on Representations of Algebras (ICRA XIV) held in Tokyo in August 2010. We first study identities between products of quantum dilogarithm series associated with Dynkin quivers following Reineke. We then examine similar identities for quivers with potential and link them to Fomin-Zelevinsky's theory of cluster algebras. Here we mainly follow ideas due to Bridgeland, Fock-Goncharov, Kontsevich-Soibelman and Nagao.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. From green mutation to $\mathrm{X}$-evolution: flows and foliations on cluster complexes

    math.RT 2025-01 conditional novelty 7.0 of 10

    Introduces a piecewise-linear flow on cluster complexes whose leaves generalize green mutation, proving these complexes are spheres for Dynkin quivers and contractible for Euclidean quivers.

  2. Contractibility and total semi-stability conditions of Euclidean quivers

    math.RT 2025-01 conditional novelty 6.0 of 10

    The moduli space of total semi-stability conditions on Euclidean quivers is described by partition data and contracts linearly to any non-concentrated stability condition.

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