Invertible braided tensor categories
| Autor: | Pavel Safronov, Adrien Brochier, Noah Snyder, David Jordan |
|---|---|
| Přispěvatelé: | University of Zurich |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Root of unity Picard group 340 Law 610 Medicine & health Witt group 01 natural sciences law.invention 510 Mathematics law Mathematics::K-Theory and Homology Tensor (intrinsic definition) Mathematics::Quantum Algebra Mathematics::Category Theory Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics Mathematics Topological quantum field theory Quantum group 010102 general mathematics Cobordism 16. Peace & justice 10123 Institute of Mathematics Invertible matrix 2608 Geometry and Topology 010307 mathematical physics Geometry and Topology |
| Zdroj: | Brochier, A, Jordan, D, Safronov, P & Snyder, N 2021, ' Invertible braided tensor categories ', Algebraic and Geometric Topology, vol. 21, no. 4, pp. 2107-2140 . https://doi.org/10.2140/agt.2021.21.2107 |
| DOI: | 10.2140/agt.2021.21.2107 |
| Popis: | We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the case of semisimple modular tensor categories, but also non-semisimple examples such as categories of representations of the small quantum group at good roots of unity. Via the cobordism hypothesis, we obtain new invertible 4-dimensional framed topological field theories, which we regard as a non-semisimple framed version of the Crane-Yetter-Kauffman invariants, after Freed--Teleman and Walker's construction in the semisimple case. More generally, we characterize invertibility for E_1- and E_2-algebras in an arbitrary symmetric monoidal oo-category, and we conjecture a similar characterization of invertible E_n-algebras for any n. Finally, we propose the Picard group of BrTens as a generalization of the Witt group of non-degenerate braided fusion categories, and pose a number of open questions about it. |
| Databáze: | OpenAIRE |
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