Repository landing page

We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.

Structure of bicentralizer algebras and inclusions of type III factors (Mathematical aspects of quantum fields and related topics)

Abstract

We investigate the structure of the relative bicentralizer algebra B(N ⊂ M, φ) for inclusions of von Neumann algebras with normal expectation where N is a type Ill₁ subfactor and φ ∈ N* is a faithful state. We first construct a canonical flow β[φ] : R*₊ ↷ B(N C M, ip) on the relative bicentralizer algebra and we show that the W*-dynamical system (B(N ⊂ M, φ), β[φ]) is independent of the choice of ip up to a canonical isomorphism. In the case when N = M, we deduce new results on the structure of the automorphism group of B(M, φ) and we relate the period of the flow β[φ] to the tensorial absorption of Powers factors. For general irreducible inclusions N ⊂ M, we relate the ergodicity of the flow β[φ] to the existence of irreducible hyperfinite subfactors in M that sit with normal expectation in N. When the inclusion N ⊂ M is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison's problem when N is amenable

Similar works

Full text

thumbnail-image

Kyoto University Research Information Repository

redirect
Last time updated on 08/08/2023

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.