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Orbifold aspects of the Longo-Rehren subfactors
- Publication Year :
- 2004
- Publisher :
- arXiv, 2004.
-
Abstract
- In this article, we will prove that the subsectors of $\alpha$-induced sectors for $M \rtimes \hat{G} \supset M$ forms a modular category, where $M \rtimes \hat{G}$ is the crossed product of $M$ by the group dual $\hat{G}$ of a finite group $G$. In fact, we will prove that it is equivalent to M\"uger's crossed product. By using this identification, we will exhibit an orbifold aspect of the quantum double of $\Delta$(not necessarily non-degenerate) obtained from a Longo-Rehren inclusion $A \supset B_\Delta$ under certain assumptions. We will apply the above description of the quantum double of $\Delta$ to the Reshetikhin-Turaev topological invariant of closed 3-manifolds, and we obtain a simpler formula, which is a degenerate version of Turaev's theorem that the Reshetikhin-Turaev invariant for the quantum double of a modular category $\hat{\Delta}$ is the product of Reshetikhin-Turaev invariant of $\hat{\Delta}$ and its complex conjugate.<br />Comment: 19 pages
- Subjects :
- Finite group
Pure mathematics
Complex conjugate
Group (mathematics)
Mathematics::Operator Algebras
Degenerate energy levels
Mathematics - Operator Algebras
Statistical and Nonlinear Physics
Geometric Topology (math.GT)
Mathematics::Geometric Topology
Mathematics - Geometric Topology
Crossed product
Product (mathematics)
Mathematics::Quantum Algebra
FOS: Mathematics
Invariant (mathematics)
Operator Algebras (math.OA)
Mathematical Physics
Orbifold
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....db3244b60294ad248afb9958273bf352
- Full Text :
- https://doi.org/10.48550/arxiv.math/0404509