Cluster algebras and Weil-Petersson forms

Michael Gekhtman, Michael Shapiro, Alek Vainshtein

Research output: Contribution to journalArticlepeer-review


In our paper [GSV], we discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper, we consider the case of a general matrix of transition exponents. Our leading idea is that a relevant geometric object in this case is a certain closed 2-form compatible with the cluster algebra structure. The main example is provided by Penner coordinates on the decorated Teichmüller space, in which case the above form coincides with the classical Weil-Petersson symplectic form.

Original languageEnglish
Pages (from-to)291-311
Number of pages21
JournalDuke Mathematical Journal
Issue number2
StatePublished - 1 Apr 2005

ASJC Scopus subject areas

  • General Mathematics


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