Starting from a (small) rigid C*-tensor category l with simple unit, we construct von Neumann algebras. These algebras are factors of type II or III lambda, lambda is an element of (0, 1]. The choice of type is tuned by the choice of Tomita structure (defined in the paper) on certain bimodules we use in the construction. If the spectrum is infinite we realize the whole tensor category as endomorphisms of these algebras. Furthermore, if the Tomita structure is trivial, the algebras that we get are an amplification of the free group factors with infinitely (possibly uncountably) many generators.

Giorgetti, L., Yuan, W. (2019). Realization of rigid C*-tensor categories via tomita bimodules. JOURNAL OF OPERATOR THEORY, 81(2), 433-479 [10.7900/jot.2018mar08.2219].

Realization of rigid C*-tensor categories via tomita bimodules

Giorgetti L.;
2019-01-01

Abstract

Starting from a (small) rigid C*-tensor category l with simple unit, we construct von Neumann algebras. These algebras are factors of type II or III lambda, lambda is an element of (0, 1]. The choice of type is tuned by the choice of Tomita structure (defined in the paper) on certain bimodules we use in the construction. If the spectrum is infinite we realize the whole tensor category as endomorphisms of these algebras. Furthermore, if the Tomita structure is trivial, the algebras that we get are an amplification of the free group factors with infinitely (possibly uncountably) many generators.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
C*-tensor category
pre-Hilbert C*-bimodule
full Fock space construction
free group factor
Advanced Grant QUEST n. 669240 “Quantum Algebraic Structures and Models”
Giorgetti, L., Yuan, W. (2019). Realization of rigid C*-tensor categories via tomita bimodules. JOURNAL OF OPERATOR THEORY, 81(2), 433-479 [10.7900/jot.2018mar08.2219].
Giorgetti, L; Yuan, W
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/249215
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