Minimizing indices of conditional expectations onto a subfactor

DOI10.2977/prims/1195174872zbMath0679.46050OpenAlexW2016428803MaRDI QIDQ1822733

Publication date: 1988

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195174872

zbMATH Keywords

subfactor factor Connes' spatial theory faithful normal conditional expectations Haagerup's theory of operator valued weight Jones' Index

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Classifications of (C^*)-algebras (46L35)

Related Items (42)

Index for von Neumann algebras with finite dimensional centers ⋮ An inclusion of type III factors with index 4 arising from an automorphism ⋮ Classification of actions of discrete Kac algebras on injective factors ⋮ Classification of amenable subfactors of type II ⋮ A planar algebraic description of conditional expectations ⋮ Classification of strongly amenable subfactors of type $III_0$ ⋮ Centrally free actions of amenable $\mathrm{C}^*$-tensor categories on von Neumann algebras ⋮ Anyonic chains - $\alpha$-induction - CFT - defects - subfactors ⋮ Channel divergences and complexity in algebraic QFT ⋮ Some ergodic properties for infinite graphs associated with subfactors ⋮ Poisson boundaries of monoidal categories ⋮ Representations of fusion categories and their commutants ⋮ $W^\ast$-representations of subfactors and restrictions on the Jones index ⋮ Infinite index extensions of local nets and defects ⋮ On induction for twisted representations of conformal nets ⋮ CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS ⋮ Minimal index of a $C^{*}$-crossed product by a finite group ⋮ Subalgebras of infinite $C^*$-algebras with finite Watatani indices. II: Cuntz-Krieger algebras ⋮ Amenable tensor categories and their realizations as AFD bimodules ⋮ Application of fusion rules to classification of subfactors ⋮ Entropy for canonical shifts. II ⋮ A remark on the minimal index of subgfactors ⋮ Commuting squares and the classification of finite depth inclusions of AFD type $\text{III}_\lambda$ factors, $\lambda\in(0,1)$ ⋮ Perturbations of intermediate C∗-subalgebras for simple C∗-algebras ⋮ Remarks on Automorphisms of Subfactors ⋮ Solitons in affine and permutation orbifolds ⋮ Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III ⋮ Approximate innerness and central triviality of endomorphisms ⋮ Variational approach to relative entropies with an application to QFT ⋮ A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras ⋮ A Galois correspondence for compact quantum group actions ⋮ Index of subfactors and statistics of quantum fields. I ⋮ A $C^*$-dynamical entropy and applications to canonical endomorphisms ⋮ Minimal index and dimension for 2-$C^*$-categories with finite-dimensional centers ⋮ On subfactors with unitary orthonormal bases ⋮ AMENABILITY AND STRONG AMENABILITY FOR FUSION ALGEBRAS WITH APPLICATIONS TO SUBFACTOR THEORY ⋮ Jones index theory by Hilbert C*-bimodules and K-theory ⋮ Yang–Baxter endomorphisms ⋮ Harmonic function spaces of probability measures on fusion algebras ⋮ Free composition of paragroups ⋮ Subalgebras of infinite $C^*$-algebras with finite Watatani indices. I: Cuntz algebras ⋮ Lattice of intermediate subalgebras

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