Mapping class group representations derived from stated skein algebras

DOI10.3842/SIGMA.2022.064MaRDI QIDQ2674838

Julien Korinman

Publication date: 14 September 2022

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.07649

zbMATH Keywords

mapping class groupsquantum Teichmüller spacesquantum moduli spacesstated skein algebras

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20) Knot theory (57K10) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Representations of the Kauffman bracket skein algebra. I: Invariants and miraculous cancellations
• Non-semi-simple TQFTs, Reidemeister torsion and Kashaev's invariants
• Quantum traces for representations of surface groups in SL\(_{2}(\mathbb C)\)
• Topological interpretations of lattice gauge field theory
• A finite set of generators for the Kauffman bracket skein algebra
• Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
• Symplectic structures associated to Lie-Poisson groups
• Quantum function algebra at roots of 1
• Group systems, groupoids, and moduli spaces of parabolic bundles
• Lectures on algebraic quantum groups
• Quantum character varieties and braided module categories
• Azumaya loci and discriminant ideals of PI algebras
• Triangular decomposition of skein algebras
• Unicity for representations of the Kauffman bracket skein algebra
• Symplectic structure of the moduli space of flat connection on a Riemann surface
• Combinatorial quantization of the Hamiltonian Chern-Simons theory. I
• Combinatorial quantization of the Hamiltonian Chern-Simons theory. II
• Two dimensional lattice gauge theory based on a quantum group
• Link invariants and combinatorial quantization of Hamiltonian Chern Simons theory
• Stated skein modules of marked 3-manifolds/surfaces, a survey
• Stated skein algebras of surfaces
• Quantum traces and embeddings of stated skein algebras into quantum tori
• Relating stated skein algebras and internal skein algebras
• Invariants of 3-manifolds via link polynomials and quantum groups
• Representations of the Kauffman bracket skein algebra. II: Punctured surfaces
• An analytic family of representations for the mapping class group of punctured surfaces
• Representation theory of Chern-Simons observables
• Decomposition of some Witten-Reshetikhin-Turaev representations into irreducible factors
• Unicity for representations of reduced stated skein algebras
• Excision of skein categories and factorisation homology
• The finiteness conjecture for skein modules
• The Witten-Reshetikhin-Turaev representation of the Kauffman bracket skein algebra
• Poisson orders, symplectic reflection algebras and representation theory
• Quasi-Poisson Manifolds
• Skein algebras of surfaces
• Integrating quantum groups over surfaces
• Dimension and Trace of the Kauffman Bracket Skein Algebra
• Mapping class group representations from non-semisimple TQFTs
• The quantum trace as a quantum non-abelianization map
• Quantum invariants of knots and 3-manifolds
• The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras