A duality map for quantum cluster varieties from surfaces

被引：25

作者：

Allegretti, Dylan G. L. ^{[1
]}

Kim, Hyun Kyu ^{[2
]}

机构：

[1] Yale Univ, Dept Math, 10 Hillhouse Ave, New Haven, CT 06511 USA

[2] Korea Inst Adv Study, Sch Math, 85 Hoegiro, Seoul 02455, South Korea

来源：

ADVANCES IN MATHEMATICS | 2017年 / 306卷

关键词：

Cluster variety; Quantization; Canonical basis; Skein algebra; REPRESENTATIONS; DILOGARITHM;

D O I：

10.1016/j.aim.2016.11.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the "quantum trace" map introduced by Bonahon and Wong. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1164 / 1208

页数：45

共 11 条

[1]

Bonahon F., 2012, ARXIV12061638MATHGT

[2] Quantum traces for representations of surface groups in SL2(C) [J].

Bonahon, Francis ;

Wong, Helen .

GEOMETRY & TOPOLOGY, 2011, 15 (03) :1569-1615

[3]

Chekhov L., 1999, ARXIVMATH9908165

[4] The quantum dilogarithm and representations of quantum cluster varieties [J].

Fock, V. V. ;

Goncharov, A. B. .

INVENTIONES MATHEMATICAE, 2009, 175 (02) :223-286

[5] Moduli spaces of local systems and higher teichmuller theory [J].

Fock, Vladimir ;

Goncharov, Alexander .

PUBLICATIONS MATHEMATIQUES DE L'IHES NO 103, 2006, 103 (1) :1-211

[6] CLUSTER ENSEMBLES, QUANTIZATION AND THE DILOGARITHM [J].

Fock, Vladimir V. ;

Goncharov, Alexander B. .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2009, 42 (06) :865-930

[7] Skein modules and the noncommutative torus [J].

Frohman, C ;

Gelca, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (10) :4877-4888

[8] Framed BPS states [J].

Gaiotto, Davide ;

Moore, Gregory W. ;

Neitzke, Andrew .

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 2013, 17 (02) :241-397

[9]

Gross M., 2014, ARXIV14111394MATHAG

[10]

Pock V. V., 2007, IRMA LECT MATH THEOR, V11, P647

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