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Operator Algebras in Rigid C*-Tensor Categories

Jones, Corey; Penneys, David

Description

In this article, we define operator algebras internal to a rigid C*-tensor category C. A C*/W*-algebra object in C is an algebra object A in ind-C whose category of free modules FreeMod(C) (A) is a C-module C*/W*-category respectively. When C = Hilb(fd), the category of finite dimensional Hilbert spaces, we recover the usual notions of operator algebras. We generalize basic representation theoretic results, such as the Gelfand-Naimark and von Neumann bicommutant theorems, along with the GNS...[Show more]

CollectionsANU Research Publications
Date published: 2017-11
Type: Journal article
URI: http://hdl.handle.net/1885/160795
Source: Communications in Mathematical Physics
DOI: 10.1007/s00220-017-2964-0

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