A duality for Hopf algebras and for subfactors. I

DOI10.1007/BF02100488zbMath0802.46075OpenAlexW2093610477MaRDI QIDQ1315005

Roberto Longo

Publication date: 7 December 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02100488

zbMATH Keywords

dualityCuntz algebrasinfinite factor\(C^*\)-categories of endomorphismsaction of a finite-dimensional Hopf algebracanonical endomorphism for an irreducible inclusion of factorsirreducible \(Q\)-systemsirreducible subfactors of finite index

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split \(W^*\)-inclusions
• Characterization of crossed product (properly infinite case)
• Endomorphisms of \(C^*\)-algebras, cross products and duality for compact groups
• Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
• Extension of Jones' theory on index of arbitrary factors
• Application of fusion rules to classification of subfactors
• A remark on the minimal index of subgfactors
• Minimal index and braided subfactors
• Simple \(C^*\)-algebras generated by isometries
• Subalgebras of infinite \(C^*\)-algebras with finite Watatani indices. I: Cuntz algebras
• Classification of subfactors: The reduction to commuting squares
• Simple injective subfactors
• Index of subfactors and statistics of quantum fields. I
• Index for subfactors
• Conditional expectations in von Neumann algebras
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• Index for 𝐶*-subalgebras
• Entropy and index for subfactors
• Une classification des facteurs de type ${\rm III}$
• Duality for crossed products of von Neumann algebras

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