Trace functionals on non-commutative deformations of moduli spaces of flat connections

2000/08/18 by Philippe Roche, Philippe Roché, Roche, Philippe +3
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic geometry #Algebraic structures and combinatorial models #Commutative property #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics #Modular equation #Moduli #Moduli of algebraic curves #Moduli space #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quantum mechanics #Riemann surface #TRACE (psycholinguistics) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0008149

arxiv created 2000/08/18 · openalex publication_date 2000/08/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe an efficient construction of a canonical non-commutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. We show that this algebra, which is a variant of the quantum moduli algebra introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche, has a trace functional which is related to the canonical trace in the formal index theory of Fedosov and Nest-Tsygan via the Verlinde formula.

Citations

• Vector bundles on curves and generalized theta functions: recent results and open problems
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• Deformation Quantization of Poisson Manifolds
• Exchange Dynamical Quantum Groups

Related

• Quantum Moduli Spaces of Flat Connections
• Quantization of moduli spaces of flat connections and Liouville theory
• Quantum tori, mirror symmetry and deformation theory
• The quantum trace as a quantum non-abelianization map
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