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Non-unitary fusion categories and their doubles via endomorphisms

Evans, David E. and Gannon, Terry 2017. Non-unitary fusion categories and their doubles via endomorphisms. Advances in Mathematics 310 , pp. 1-43. 10.1016/j.aim.2017.01.015

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We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup-Izumi family of Q-systems. For example, we construct endomorphism realisations of the (non-unitary) Yang-Lee model, and non-unitary analogues of one of the even subsystems of the Haagerup subfactor and of the Grossman-Snyder system. We supplement Izumi's equations for identifying the half-braidings, which were incomplete even in his Q-system setting. We conjecture a remarkably simple form for the modular S and T matrices of the doubles of these fusion categories. We would expect all of these doubles to be realised as the category of modules of a rational VOA and conformal net of factors. We expect our approach will also suffice to realise the non-semisimple tensor categories arising in logarithmic conformal field theories.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Modular tensor categories; Non-unitary; Leavitt algebra; Quantum double; Conformal field theory; Subfactor
Additional Information: This is an open access article under the CC BY license (
Publisher: Elsevier
ISSN: 0001-8708
Funders: EPSRC
Date of First Compliant Deposit: 6 February 2017
Date of Acceptance: 17 January 2017
Last Modified: 17 Nov 2020 12:00

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