Cluster algebras and Weil-Petersson forms

Cluster algebras and Weil-Petersson forms

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...

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Veröffentlicht in:Duke mathematical journal 2005-04, Vol.127 (2), p.291-311
Hauptverfasser: Gekhtman, Michael, Shapiro, Michael, Vainshtein, Alek
Format: Artikel
Sprache:eng
Schlagworte:
14M20
30Fxx
32G15
53D17
53D30
Moduli of Riemann surfaces
Poisson groupoids and algebroids
Poisson manifolds
Rational and unirational varieties [See also 14E08]
Symplectic structures of moduli spaces
Teichmüller theory [See also 14H15
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Shapiro, Michael
Vainshtein, Alek
description 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.
doi_str_mv 10.1215/S0012-7094-04-12723-X
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ispartof Duke mathematical journal, 2005-04, Vol.127 (2), p.291-311
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1547-7398
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subjects 14M20
30Fxx
32G15
53D17
53D30
Moduli of Riemann surfaces
Poisson groupoids and algebroids
Poisson manifolds
Rational and unirational varieties [See also 14E08]
Symplectic structures of moduli spaces
Teichmüller theory [See also 14H15
title Cluster algebras and Weil-Petersson forms
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