Abstract
We introduce the notion of Q-systems as Frobenius algebras in a C* tensor category, enjoying a standardness property. Q-systems in the category of endomorphisms of an infinite factor \(N\) completely characterize extensions \(N\subset M\). Modules and bimodules of Q-systems are equivalent to homomorphisms \(N\rightarrow M\) resp. \(M_1\rightarrow M_2\).
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Notes
- 1.
The term factorial might be more appropriate in this context. “Simple”, however, is more in line with standard category terminology, cf. Corollary 3.40.
- 2.
More precisely, \((\beta ,m^*)\) is a module and \((\beta ,m)\) is a co-module. We do not make the distinction because the dualization is canonically given by the operator adjoint.
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Bischoff, M., Kawahigashi, Y., Longo, R., Rehren, KH. (2015). Frobenius Algebras, Q-Systems and Modules. In: Tensor Categories and Endomorphisms of von Neumann Algebras. SpringerBriefs in Mathematical Physics, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-14301-9_3
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