Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of algebraic relations and of zero divisors under the assumption
  of full non-microstates free entropy dimension   We show that in a tracial and finitely generated $W^\ast$-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.

20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg