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.
引用
收藏
页码：1164 / 1208
页数：45
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