Quantum Teichmüller space from quantum plane

Details Quantum Teichmüller space from quantum plane Quantum Teichmüller space from quantum plane

2010-06-19

arxiv.org/abs/1006.3895v1

Mathematics

Representation Theory

41 pages, 9 figures

Scientific paper

We derive the quantum Teichm\"uller space, previously constructed by Kashaev and by Fock and Chekhov, 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. We also show that the quantum universal Teichm\"uller space is realized in the infinite tensor power of the canonical representation naturally indexed by rational numbers including the infinity. This suggests a relation to the same index set in the classification of projective modules over the quantum torus, the unitary counterpart of the quantum plane, and points to a new quantization of the universal Teichm\"uller space.

Affiliated with

Also associated with

No associations

Rating

Quantum Teichmüller space from quantum plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Teichmüller space from quantum plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Teichmüller space from quantum plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-185741