Abstract:
We investigate the structure of the Longo–Rehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the Longo–Rehren inclusions in terms of half braidings, which do not necessarily satisfy the usual condition of braidings. In doing so, we give new proofs to most of the known statements concerning asymptotic inclusions. We construct a complete system of matrix units of the tube algebra using the half braidings, which will be used in the second part to describe concrete examples of the Longo–Rehren inclusions arising from the Cuntz algebra endomorphisms. We also discuss the case where the original system has a braiding, and generalize Ocneanu and Evans–Kawahigashi's method for the analysis of the asymptotic inclusions of the Hecke algebra subfactors.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 19 July 1999 / Accepted: 10 February 2000
Rights and permissions
About this article
Cite this article
Izumi, M. The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory. Commun. Math. Phys. 213, 127–179 (2000). https://doi.org/10.1007/s002200000234
Issue Date:
DOI: https://doi.org/10.1007/s002200000234