41 citations · 111 across the 22 of their papers we have counts for
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Naturality of quantum trace maps for surfaces
Hyun Kyu Kim
Fock-Goncharov's moduli spaces of framed -local systems on punctured surfaces provide prominent examples of cluster $\m…
Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
Hyun Kyu Kim
Representation theory of the quantum torus Hopf algebra, when the parameter is a root of unity, is studied. We investigate a decomposition map of the tensor product of two irre…
Comments on Exchange Graphs in Cluster Algebras
Hyun Kyu Kim, Masahito Yamazaki
An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, gene…
Phase constants in the Fock-Goncharov quantization of cluster varieties: long version
Hyun Kyu Kim
A cluster variety of Fock and Goncharov is a scheme constructed from the data related to the cluster algebras of Fomin and Zelevinsky. A seed is a combinatorial data which can be e…
Phase constants in the Fock-Goncharov quantum cluster varieties
Hyun Kyu Kim
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, th…
A duality map for quantum cluster varieties from surfaces
Dylan G. L. Allegretti, Hyun Kyu Kim
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…