Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension☆,☆☆
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MSC
46L54
60B20
Keywords
Free probability theory
Conjugate variables
Free Fisher information
Non-microstates free entropy dimension
Algebraic relations
Zero divisors
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This work was supported by the ERC Advanced Grant “Non-commutative distributions in free probability” (grant no. 339760) and by a grant from the DFG (SP-419-8/1).
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We thank H. Bercovici, Y. Dabrowski and D. Shlyakhtenko for discussions and comments on an earlier version of this paper. Furthermore, we want to express our gratitude to an anonymous referee for carefully reading the manuscript and his valuable comments.
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