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1 April 2005 Cluster algebras and Weil-Petersson forms
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
Duke Math. J. 127(2): 291-311 (1 April 2005). DOI: 10.1215/S0012-7094-04-12723-X

Abstract

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.

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Michael Gekhtman. Michael Shapiro. Alek Vainshtein. "Cluster algebras and Weil-Petersson forms." Duke Math. J. 127 (2) 291 - 311, 1 April 2005. https://doi.org/10.1215/S0012-7094-04-12723-X

Information

Published: 1 April 2005
First available in Project Euclid: 23 March 2005

zbMATH: 1079.53124
MathSciNet: MR2130414
Digital Object Identifier: 10.1215/S0012-7094-04-12723-X

Subjects:
Primary: 53D17
Secondary: 14M20, 32G15, 53D30

Rights: Copyright © 2005 Duke University Press

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Vol.127 • No. 2 • 1 April 2005
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