منابع مشابه
On representing some lattices as lattices of intermediate subfactors of finite index
We prove that the very simple lattices which consist of a largest, a smallest and 2n pairwise incomparable elements where n is a positive integer can be realized as the lattices of intermediate subfactors of finite index and finite depth. Using the same techniques, we give a necessary and sufficient condition for subfactors coming from Loop groups of type A at generic levels to be maximal. Supp...
متن کاملConformal Subnets and Intermediate Subfactors
Given an irreducible local conformal net A of von Neumann algebras on S1 and a finite-index conformal subnet B ⊂ A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu for the orbifold construction. By applying previous results of Xu, many coset models turn out to be completely rational and the structure results in [27] hold. Our proo...
متن کاملIntermediate Subfactors with No Extra Structure
Let N ⊆ M be II1 factors with [M : N ] < ∞. There is a “standard invariant” for N ⊆ M , which we shall describe using the planar algebra formalism of [19]. The vector spaces Pk of N −N invariant vectors in the N −N bimodule ⊗M admit an action of the operad of planar tangles as in [19] and [21]. In more usual notation the vector space Pk is the relative commutant N ′ ∩Mk−1 in the tower Mk of [16...
متن کاملOn Examples of Intermediate Subfactors from Conformal Field Theory
Motivated by our subfactor generalization of Wall’s conjecture, in this paper we determine all intermediate subfactors for conformal subnets corresponding to four infinite series of conformal inclusions, and as a consequence we verify that these series of subfactors verify our conjecture. Our results can be stated in the framework of Vertex Operator Algebras. We also verify our conjecture for J...
متن کاملFuss-catalan Algebras and Chains of Intermediate Subfactors
We give a complete description of the generalized FussCatalan algebras: colored generalizations of the TemperleyLieb algebras, introduced by D. Bisch and V. Jones. For these chains of finite dimensional algebras, we describe a basis in terms of generators, and give a complete description, including the dimensions, of the irreducible representations. We then consider an arbitrary subfactor conta...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1996
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0110