Quantum Teichmüller space from quantum plane - II

This is the continuation of the talk given on Oct 4. Last time I presented
Kashaev’s construction of the quantum Teichmüller space. In this second part of the talk, I’ll show how we derive the same result from tensor products of a
single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the
decomposition of the tensor square, the quantum mutation operator arises from the tensor cube, the pentagon identity from the tensor fourth power of the canonical representation, and an operator of order three from isomorphisms between canonical representation and its left and right duals.
If time allows, I’ll also talk about quantum universal Teichmüller space, and a
candidate for new quantization of the universal Teichmüller space coming from projective modules over the quantum torus. This is a joint work with I. B.
Frenkel.