Abstract
The q-deformed Araki-Woods von Neumann algebras \(\Gamma _q({\mathcal {H}}_{\mathbb {R}},U_t)^{\prime \prime }\) are factors for all \(q\in (-1,1)\) whenever dim\(({\mathcal {H}}_{\mathbb {R}})\ge 3\). When dim\(({\mathcal {H}}_{\mathbb {R}})=2\) they are factors as well for all q so long as the parameter defining \((U_t)\) is ‘small’ or 1 (trivial) as the case may be.
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Acknowledgements
P. Bikram, K. Mukherjee and É. Ricard acknowledge the support of the grant 6101-1 from the CEFIPRA. É. Ricard is also supported by ANR-19-CE40-0002. S. Wang would like to thank C. Houdayer and M. Wasilewski for fruitful discussions at the early stage of this project. S. Wang is also supported by the Fundamental Research Funds for the Central Universities No. FRFCUAUGA5710012222 and NSF of China No. 12031004.
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Bikram, P., Mukherjee, K., Ricard, É. et al. On the Factoriality of q-Deformed Araki-Woods von Neumann Algebras. Commun. Math. Phys. 398, 797–821 (2023). https://doi.org/10.1007/s00220-022-04535-2
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DOI: https://doi.org/10.1007/s00220-022-04535-2