2002/01/15 by Razvan Gelca, Răzvan Gelca, Gelca, Razvan · 1 citation
Mathematics · #57M27 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0201122
Latex, 10 pages, 2 figures
arxiv created 2002/01/15 · openalex publication_date 2002/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper exhibits a product-to-sum formula for the observables of a certain quantization of the moduli space of flat SU(2)-connections on the torus. This quantization was defined using the topological quantum field theory that was developed by Reshetikhin and Turaev from the quantum group of SL(2,C) at roots of unity. As a corollary it is shown that the algebra of quantum observables is a subalgebra of the noncommutative torus with rational rotation angle. The proof uses topological quantum field theory with corners, and is based on the description of the matrices of the observables in a canonical basis of the Hilbert space of the quantization.