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Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules

Aaserud, Andreas Naes and Evans, David E. 2020. Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules. Communications in Mathematical Physics 380 , pp. 103-130. 10.1007/s00220-020-03729-w

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Abstract

We associate to each Temperley-Lieb-Jones C*-tensor category TLJcat(delta) with parameter delta in the discrete range {2\cos(\pi/(k+2)),: ,k=1,2, ...} or 2 a certain C*-algebra B of compact operators. We use the unitary braiding on TLJcat(delta) to equip the category ModB of (right) Hilbert B-modules with the structure of a braided C*-tensor category. We show that TLJcat(delta) is equivalent, as a braided C*-tensor category, to the full subcategory of ModB whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Springer Verlag
ISSN: 0010-3616
Funders: EPSRC
Date of First Compliant Deposit: 11 February 2020
Date of Acceptance: 4 February 2020
Last Modified: 21 Jan 2021 11:45
URI: http://orca.cf.ac.uk/id/eprint/129424

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