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Cluster algebras and Weil-Petersson forms. (English) Zbl 1079.53124
Duke Math. J. 127, No. 2, 291-311 (2005); correction 139, No. 2, 407-409 (2007).
The authors discuss properties of cluster algebras for the case of a general matrix of transition exponents. This paper is a continuation of a preceding work where the authors introduced a Poisson formalism compatible with cluster algebras. Motivated by the study of dual canonical bases and the theory of double Bruhat cells, the authors work here with a certain closed two-form compatible with the cluster algebra structure. The construction is then applied to the coordinate ring of the Teichmüller space. The Weil Petersson symplectic form is recovered in this context.
From the text of the correction: We provide correction to the formulation and the proof of Theorem 3.4 in the original article. (added in 2009)

MSC:
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D10 Contact manifolds (general theory)
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