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Phase constants in the Fock–Goncharov quantum cluster varieties

Title
Phase constants in the Fock–Goncharov quantum cluster varieties
Authors
Kim H.K.
Ewha Authors
김현규
SCOPUS Author ID
김현규scopus
Issue Date
2021
Journal Title
Analysis and Mathematical Physics
ISSN
1664-2368JCR Link
Citation
Analysis and Mathematical Physics vol. 11, no. 1
Publisher
Birkhauser
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to non-commutative rings, represented as operators on Hilbert spaces. Mutations are quantized to unitary maps between the Hilbert spaces intertwining the representations. These unitary intertwiners are described using the quantum dilogarithm function Φ ħ. Algebraic relations among classical mutations are satisfied by the intertwiners up to complex constants. The present paper shows that these constants are 1. So the mapping class group representations resulting from the Chekhov–Fock–Goncharov quantum Teichmüller theory are genuine, not projective. During the course, the hexagon and the octagon operator identities for Φ ħ are derived. © 2020, Springer Nature Switzerland AG.
DOI
10.1007/s13324-020-00439-3
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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