Corpus ID: 159040890

The free field: realization via unbounded operators and Atiyah property

@article{Mai2019TheFF,
  title={The free field: realization via unbounded operators and Atiyah property},
  author={Tobias Mai and R. Speicher and Sheng Yin},
  journal={arXiv: Operator Algebras},
  year={2019}
}
Let $X_1,\dots,X_n$ be operators in a finite von Neumann algebra and consider their division closure in the affiliated unbounded operators. We address the question when this division closure is a skew field (aka division ring) and when it is the free skew field. We show that the first property is equivalent to the strong Atiyah property and that the second property can be characterized in terms of the non-commutative distribution of $X_1,\dots,X_n$. More precisely, $X_1,\dots,X_n$ generate the… Expand

References

SHOWING 1-10 OF 44 REFERENCES
Non-commutative rational function in strongly convergent random variables
A Deterministic Polynomial Time Algorithm for Non-commutative Rational Identity Testing
...
1
2
3
4
5
...