A duality map for quantum cluster varieties from surfaces

被引：21
|
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.
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页码：1164 / 1208
页数：45
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