کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424934 1633784 2017 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension
چکیده انگلیسی

We show that in a tracial and finitely generated W⁎-probability space existence of conjugate variables excludes algebraic relations for the generators. Moreover, under the assumption of maximal non-microstates free entropy dimension, we prove that there are no zero divisors in the sense that the product of any non-commutative polynomial in the generators with any element from the von Neumann algebra is zero if and only if at least one of those factors is zero. In particular, this shows that in this case the distribution of any non-constant self-adjoint non-commutative polynomial in the generators does not have atoms.Questions on the absence of atoms for polynomials in non-commuting random variables (or for polynomials in random matrices) have been an open problem for quite a while. We solve this general problem by showing that maximality of free entropy dimension excludes atoms.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 304, 2 January 2017, Pages 1080-1107
نویسندگان
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