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arXiv · 1407.5715

Absence of algebraic relations and of zero divisors under the assumption of finite non-microstates free Fisher information

Tobias Mai·Roland Speicher·Moritz Weber
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Abstract

We show that in a tracial and finitely generated $W^\ast$-probability space existence of conjugate variables in an appropriate sense exclude algebraic relations for the generators. Moreover, under the assumption of finite non-microstates free Fisher information, 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.

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Tobias Mai, Roland Speicher, Moritz Weber. 2015-02-22. Absence of algebraic relations and of zero divisors under the assumption of finite non-microstates free Fisher information. https://arxiv.org/abs/1407.5715

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