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math.RT2021★ 2 cited
Three-dimensional quantum gravity from the quantum pseudo-Kähler plane
Hyun Kyu Kim
A new canonical Hopf algebra called the quantum pseudo-Kähler plane is introduced. This quantum group can be viewed as a deformation quantization of the complex two-dimensional pla…
math.RT2020★ 1 cited
Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants
Hyun Kyu Kim
Quantization of the Teichmüller space of a non-compact Riemann surface has emerged in 1980's as an approach to three dimensional quantum gravity. For any choice of an ideal triangu…
math.RT2010★ 14 cited
Quantum Teichmüller space from quantum plane
Igor B. Frenkel, Hyun Kyu Kim
We derive the quantum Teichmüller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double…