Mapping class group representations from non-semisimple TQFTs
| Autor: | Nathan Geer, Ingo Runkel, Marco De Renzi, Bertrand Patureau-Mirand, Azat M. Gainutdinov |
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| Přispěvatelé: | Institute of Mathematics University of Zurich, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Department of Mathematics and Statistics [Logan], Utah State University (USU), Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Brest (UBO)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS), Fachbereich Mathematik [Hamburg], Universität Hamburg (UHH), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), University of Zurich, De Renzi, Marco |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Class (set theory) Pure mathematics General Mathematics FOS: Physical sciences Set (abstract data type) Mathematics - Geometric Topology 510 Mathematics 2604 Applied Mathematics [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] Mathematics::Category Theory Mathematics::Quantum Algebra Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Quantum field theory Algebraic number 2600 General Mathematics Mathematics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Quantum group Applied Mathematics Order (ring theory) Geometric Topology (math.GT) Action (physics) Mapping class group 10123 Institute of Mathematics High Energy Physics - Theory (hep-th) [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] |
| Zdroj: | HAL |
| ISSN: | 1793-6683 0219-1997 |
| DOI: | 10.1142/s0219199721500917 |
| Popis: | In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by these TQFTs, and we express the action of a set of generators through the algebraic data of the underlying modular category $\mathcal{C}$. This allows us to prove that the projective representations induced from the non-semisimple TQFTs of [arXiv:1912.02063] are equivalent to those obtained by Lyubashenko via generators and relations in [arXiv:hep-th/9405167]. Finally, we show that, when $\mathcal{C}$ is the category of finite-dimensional representations of the small quantum group of $\mathfrak{sl}_2$, the action of all Dehn twists for surfaces without marked points has infinite order. 41 pages, minor corrections, Section 2.4 and Appendix C added |
| Databáze: | OpenAIRE |
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