Comments on Exchange Graphs in Cluster Algebras
- 주제(키워드) Cluster algebra , dilogarithm identity , exchange graph
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Taylor and Francis Inc.
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000168820
- 본문언어 영어
- Published As https://dx.doi.org/10.1080/10586458.2018.1437849
초록/요약
An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds. © 2018, © 2018 Taylor & Francis Group, LLC.
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