An application of free transport to mixed q-gaussian algebras

Brent Nelson University of California, Berkeley Qiang Zeng Harvard University CMSA

Publications of CMSA of Harvard mathscidoc:1702.38075

We consider the mixed q-Gaussian algebras introduced by Speicher which are generated by the variables Xi = li + l ∗ i , i = 1, . . . , N, where l ∗ i lj − qij lj l ∗ i = δi,j and −1 < qij = qji < 1. Using the free monotone transport theorem of Guionnet and Shlyakhtenko, we show that the mixed q-Gaussian von Neumann algebras are isomorphic to the free group von Neumann algebra L(FN ), provided that maxi,j |qij | is small enough. Similar results hold in the reduced C ∗ -algebra setting. The proof relies on some estimates which are generalizations of Dabrowski’s results for the special case qij ≡ q.
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@inproceedings{brentan,
  title={AN APPLICATION OF FREE TRANSPORT TO MIXED q-GAUSSIAN ALGEBRAS},
  author={Brent Nelson, and Qiang Zeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208004753546961302},
}
Brent Nelson, and Qiang Zeng. AN APPLICATION OF FREE TRANSPORT TO MIXED q-GAUSSIAN ALGEBRAS. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208004753546961302.
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