Finite dimensional approximation of pairs of algebras and obstructions for the index

DOI10.1016/0022-1236(91)90079-KzbMath0746.46052OpenAlexW2049595871MaRDI QIDQ1174963

Sorin Popa, Mihai V. Pimsner

Publication date: 25 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(91)90079-k

zbMATH Keywords

relative entropygeneralized indexsubfactor of the hyperfinite \(II_ 1\) factorsubfactors having finite Jones' index

Mathematics Subject Classification ID

Subfactors and their classification (46L37) Classifications of (C^*)-algebras (46L35)

Related Items (16)

Classification of amenable subfactors of type II ⋮ Subfactors with principal graph \(E_ 6^{(1)}\) ⋮ A planar algebraic description of conditional expectations ⋮ The legacy of Vaughan Jones in 𝐼𝐼₁ factors ⋮ Some ergodic properties for infinite graphs associated with subfactors ⋮ Poisson boundaries of monoidal categories ⋮ On orthogonal systems, two-sided bases, and regular subfactors ⋮ \(W^\ast\)-representations of subfactors and restrictions on the Jones index ⋮ \(C^\ast\)-algebras from planar algebras. II: The Guionnet-Jones-Shlyakhtenko \(C^\ast\)-algebras ⋮ Entropy of groups and subfactors ⋮ Entropy for canonical shifts. II ⋮ A note on irreducible quadrilaterals of II1 factors ⋮ Minimal index and dimension for 2-\(C^*\)-categories with finite-dimensional centers ⋮ Subfactors of index exactly 5 ⋮ Irreducible subfactors from some symmetric graphs ⋮ Towards a Classification of Compact Quantum Groups of Lie Type

Cites Work

• Maximal injective subalgebras in factors associated with free groups
• Relative dimension, towers of projections and commuting squares of subfactors
• Hecke algebras of type \(A_ n\) and subfactors
• Cohomology and extensions of von Neumann algebras. II
• Entropy for automorphisms of \(II_1\) von Neumann algebras
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Subalgebras of a finite algebra
• Classification of subfactors: The reduction to commuting squares
• Index for subfactors
• On rings of operators. IV
• Iterating the Basic Construction
• Entropy and index for subfactors
• Central Sequences and the Hyperfinite Factor
• A $\mathrm{II}_1$ factor anti-isomorphic to itself but without involutory antiautomorphisms.
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