Quantum Dilogarithm Identities at Root of Unity

2014/12/18 by Ivan Chi-Ho Ip, Masahito Yamazaki · 1 voice
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th #math.QA #msc:13F60

paper · pdf · doi:10.1093/imrn/rnv141

published as Int. Math. Res. Notices. 2016, 669 (2016) · 20 pages

arxiv created 2014/12/18 · arxiv published 2014/12/18 · arxiv updated 2014/12/18 · openalex publication_date 2015/05/20 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

We study the root of unity degeneration of cluster algebras and quantum dilogarithm identities. We prove identities for the cyclic dilogarithm associated with a mutation sequence of a quiver, and as a consequence new identities for the non-compact quantum dilogarithm at b=1.

Citations

• Current-Like Variables in Massive and Massless Integrable Models
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Cluster algebras IV: Coefficients
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

Discussions

• 今週は数学の論文の執筆に熱中、今回は最初から最後までひたすら数学だったので数学の研究の勉強になった。今後は数学者を名乗ってもいいだろうか？論文は http://arxiv.org/abs/1412.5777 [bsky, 0 points, 0 comments]

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