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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
