Free entropy and property T factors.
نویسندگان
چکیده
We show that a large class of finite factors has free entropy dimension less than or equal to one. This class includes all prime factors and many property T factors.
منابع مشابه
v 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 کاملFree Diffusions, Free Entropy and Free Fisher Information
Motivated by the stochastic quantization approach to large N matrix models, we study solutions to free stochastic diierential equations dX t = dS t ? 1 2 f (X t)dt where S t is a free brownian motion. We show existence, uniqueness and Markov property of solutions. We deene a relative free entropy as well as a relative free Fisher information, and show that these quantities behave as in the clas...
متن کاملFurstenberg Entropy Realizations for Virtually Free Groups and Lamplighter Groups
Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...
متن کاملFree Entropy Dimension 1 for Some Generators ofProperty T Factors of Type II
The modified free entropy dimension of certain n-tuples of self-adjoint operators, satisfying sequential commutation, is shown to be ≤ 1. In particular the von Neumann algebras of type II1 of the groups SL(n,Z), n ≥ 3 have generators with free entropy dimension ≤ 1. The free entropy χ(X1, . . . , Xn) and the modified free entropy dimension δ0(X1, . . . , Xn) of an n-tuple of selfadjoint element...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 97 18 شماره
صفحات -
تاریخ انتشار 2000