A duality map for quantum cluster varieties from surfaces

Dylan G.L. Allegretti; Hyun Kyu Kim

doi:10.1016/j.aim.2016.11.007

A duality map for quantum cluster varieties from surfaces

Dylan G.L. Allegretti, Hyun Kyu Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1164-1208
Number of pages	45
Journal	Advances in Mathematics
Volume	306
DOIs	https://doi.org/10.1016/j.aim.2016.11.007
State	Published - 14 Jan 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Canonical basis
Cluster variety
Quantization
Skein algebra

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10.1016/j.aim.2016.11.007

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abstract = "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.",

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AU - Kim, Hyun Kyu

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AB - 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.

KW - Canonical basis

KW - Cluster variety

KW - Quantization

KW - Skein algebra

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DO - 10.1016/j.aim.2016.11.007

M3 - Article

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A duality map for quantum cluster varieties from surfaces

Abstract

Bibliographical note

Keywords

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