منابع مشابه
Kadison-Singer algebras: hyperfinite case.
A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...
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We construct a series of inclusions of hyperfinite subfactors Pi in the centralizer R of Powers’ IIIt factor, Pi+1 ⊂ Pi ⊂ R. It is proven that: ∀i ∈ N, P ′ i ∩R = C, [Pi : Pi+1] ≥ λ = (1 + t) t Via an outer action of Z2 on R, we also construct an inclusion of hyperfinite II1 factors, M3 ⊂ M1 with the index equal to λ, such that the relative commutant M1 ∩M ′ 3 is four dimensional.
متن کاملInnerness of ρ-derivations on Hyperfinite Von Neumann Algebras
Suppose that M,N are von Neumann algebras acting on a Hilbert space and M is hyperfinite. Let ρ : M → N be an ultraweakly continuous ∗-homomorphism and let δ : M → N be a ∗-ρ-derivation such that δ(I) commutes with ρ(I). We prove that there is an element U in N with ‖U‖ ≤ ‖δ‖ such that δ(A) = Uρ(A)− ρ(A)U for all A ∈ M. c © Electronic Journal of Theoretical Physics. All rights reserved.
متن کاملRemarks on Finite W Algebras
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≃ so(4, 2), unitary representations of the conformal and Poincaré algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G ≃ sp(2,R) or sp(4,R ), the anyonic parameter can be se...
متن کاملThe Free Entropy Dimension of Hyperfinite Von Neumann Algebras
ABSTRACT. Suppose M is a hyperfinite von Neumann algebra with a tracial state φ and {a1, . . . , an} is a set of self-adjoint generators for M. We calculate δ0(a1, . . . , an), the modified free entropy dimension of {a1, . . . , an}. Moreover we show that δ0(a1, . . . , an) depends only on M and φ. Consequently δ0(a1, . . . , an) is independent of the choice of generators for M . In the course ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0328618-9