On the Structure of Finite Depth Subfactors

Dietmar Bisch
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Dietmar Bisch: Mathematical Sciences Research Institute

A chapter in Algebraic Methods in Operator Theory, 1994, pp 175-194 from Springer

Abstract: Abstract We study the basic construction of a pair of reduced subfactors N p ⊂ pM p, p ∈ N 1 ⋂ M a projection and provide a method of computing the graphs of the reduced subfactors using the Bratteli diagrams of the original inclusion N ⊂ M. Then we describe what we mean by a fusion algebra associated to a subfactor and explain how these fusion algebras can be computed explicitly. In particular this provides an explicit method of calculating the graphs of the reduced subfactors. We present the results of these computations for various subfactors such as for the 3+√3 subfactor and for Haagerup’s smallest finite depth subfactor of the hyperfinite II1 factor with index above 4.

Keywords: Braid Group; Conformal Field Theory; Fusion Rule; Multiplication Table; Basic Construction (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_19

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DOI: 10.1007/978-1-4612-0255-4_19

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