From a Kac algebra subfactor to Drinfeld double

Article Type

Research Article

Publication Title

Journal of Mathematical Physics

Abstract

Given a finite-index and finite-depth subfactor, we define the notion of quantum double inclusion - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of Ocneanu's asymptotic inclusion. We show that the quantum double inclusion when applied to the Kac algebra subfactor RH ⊂ R produces Drinfeld double of H, where H is a finite-dimensional Kac algebra acting outerly on the hyperfinite II1 factor R and RH denotes the fixed-point subalgebra. More precisely, quantum double inclusion of RH ⊂ R is isomorphic to R ⊂ R × D(H)cop for some outer action of D(H)cop on R, where D(H) denotes the Drinfeld double of H.

DOI

10.1063/1.5095497

Publication Date

7-1-2019

Comments

Open Access, Green

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