Infinite Multiplicity of Abelian Subalgebras in Free Group Subfactors
نویسنده
چکیده
We obtain an estimate of Voiculescu’s (modified) free entropy dimension for generators of a II1-factor M with a subfactor N containing an abelian subalgebra A of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.
منابع مشابه
Indecomposability of Free Group Factors over Nonprime Subfactors and Abelian Subalgebras
Abstract. We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian ∗-subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group...
متن کاملAn Estimate of Free Entropy and Applications
We obtain an estimate of free entropy of generators in a type II1-factor M which has a subfactor N of finite index with a subalgebra P = P1∨P2 ⊂ N where P1 = R1∩P , P2 = R2∩P are diffuse, R1,R2 ⊂ P are mutually commuting hyperfinite subfactors, and an abelian subalgebra A ⊂ N such that the correspondence PL 2(N , τ)A is M-weakly contained in a subcorrespondence PHA of PL 2(M, τ)A, generated by ...
متن کاملv 1 8 M ay 1 99 6 TWO APPLICATIONS OF FREE ENTROPY Kenneth
In [8] and [9], Voiculescu introduced free entropy for n–tuples of self–adjoint elements in a II1–factor, and used it to prove that free group factors, L(Fn), lack Cartan subalgebras [9]. In [4], S. Popa introduced a property for II1–factors, called property C. (See [5] for a paper related to [4].) Like Property Γ of Murray and von Neumann, this is an asymptotic commutivity property, but it is ...
متن کاملar X iv : f un ct - a n / 96 05 00 5 v 2 1 2 Se p 19 96 TWO APPLICATIONS OF FREE ENTROPY
Using Voiculsecu’s free entropy, it is shown that the free group factors L(Fn) lack property C of Popa and that they lack finite multiplicity abelian subalgebras.
متن کاملInfinite Abelian Subalgebras in Quantum W-Algebras: An Elementary Proof
An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all principle W-algebras associated with the simple Lie algebras. The proof is based on the more general result that for a class of vertex operators the quantum...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004