منابع مشابه
Some Free Entropy Dimension Inequalities for Subfactors
Suppose N ⊂ M is an inclusion of II1-factors of finite index. If N can be generated by a finite set of elements, then there exist finite generating sets X for N and Y for M such that δ0(X) ≥ δ0(Y ), where δ0 denotes Voiculescu’s microstates (modified) free entropy dimension. Moreover, given ǫ > 0 one has δ0(F ) ≥ δ0(G) ≥ ([M : N ] −2 − ǫ) · (δ0(F ) − 1) + 1 − ǫ for certain generating sets F for...
متن کاملSubfactors of index exactly 5
We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from work of Izumi in preparation. The non-existence results build upon the classification of subfactor planar algebras with index less than 5, with some additional analysis of special cases.
متن کاملOn Hyperfinite Ii1 Subfactors of Finite Jones Index
We consider certain conditions for abstract lattices of commuting squares, that we prove are necessary and sufficient for them to arise as lattices of higher relative commutants of hyperfinite II1 inclusions of finite Jones index. In particular, we construct a one parameter family of inclusions of hyperfinite II1 factors N ⊂ M, with trivial relative commutant (Nλ)′∩Mλ = C with the Jones index [...
متن کاملThe Classification of Subfactors of Index at Most 5
A subfactor is an inclusion N ⊂ M of von Neumann algebras with trivial centers. The simplest example comes from the fixed points of a group action M ⊂M , and subfactors can be thought of as fixed points of more general group-like algebraic structures. These algebraic structures are closely related to tensor categories and have played important roles in knot theory, quantum groups, statistical m...
متن کاملStrong Singularity for Subfactors
We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its unitary conjugate. Through planar algebra techniques, we demonstrate the existence of a finite index singular subfactor of the hyperfinite II1 factor that cannot be st...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1986
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1504