Singularity of the generator subalgebra in $q$-Gaussian algebras
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Abstract:
Given $-1<q<1$ and a separable real Hilbert space $\mathcal {H}_{\mathbb {R}}$ with dimension no less than 2, we prove that the generator subalgebra in the $q$-Gaussian algebra $\Gamma _q(\mathcal {H}_{\mathbb {R}})$ is singular.References
- Stephen Avsec, Strong solidity of the $q$-Gaussian algebras for all $-1< q< 1$, arXiv:1110.4918, 2011.
- Panchugopal Bikram and Kunal Mukherjee, Generator masas in $q$-deformed Araki-Woods von Neumann algebras and factoriality, arXiv:1606.04752, 2016.
- Marek Bożejko and Roland Speicher, An example of a generalized Brownian motion, Comm. Math. Phys. 137 (1991), no. 3, 519–531. MR 1105428
- Marek Bożejko and Roland Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Ann. 300 (1994), no. 1, 97–120. MR 1289833, DOI 10.1007/BF01450478
- A. Guionnet and D. Shlyakhtenko, Free monotone transport, Invent. Math. 197 (2014), no. 3, 613–661. MR 3251831, DOI 10.1007/s00222-013-0493-9
- Paul Jolissaint and Yves Stalder, Strongly singular MASAs and mixing actions in finite von Neumann algebras, Ergodic Theory Dynam. Systems 28 (2008), no. 6, 1861–1878. MR 2465603, DOI 10.1017/S0143385708000072
- Alexandre Nou, Non injectivity of the $q$-deformed von Neumann algebra, Math. Ann. 330 (2004), no. 1, 17–38. MR 2091676, DOI 10.1007/s00208-004-0523-4
- Sorin Popa, Maximal injective subalgebras in factors associated with free groups, Adv. in Math. 50 (1983), no. 1, 27–48. MR 720738, DOI 10.1016/0001-8708(83)90033-6
- Éric Ricard, Factoriality of $q$-Gaussian von Neumann algebras, Comm. Math. Phys. 257 (2005), no. 3, 659–665. MR 2164947, DOI 10.1007/s00220-004-1266-5
- Allan M. Sinclair and Roger R. Smith, Finite von Neumann algebras and masas, London Mathematical Society Lecture Note Series, vol. 351, Cambridge University Press, Cambridge, 2008. MR 2433341, DOI 10.1017/CBO9780511666230
- Chenxu Wen, Maximal amenability and disjointness for the radial masa, J. Funct. Anal. 270 (2016), no. 2, 787–801. MR 3425903, DOI 10.1016/j.jfa.2015.08.013
Additional Information
- Chenxu Wen
- Affiliation: Department of Mathematics, University of California, Riverside, California 92521
- MR Author ID: 1136545
- Email: chenxuw@ucr.edu
- Received by editor(s): June 29, 2016
- Received by editor(s) in revised form: September 12, 2016, and September 18, 2016
- Published electronically: January 26, 2017
- Communicated by: Adrian Ioana
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3493-3500
- MSC (2010): Primary 46L10
- DOI: https://doi.org/10.1090/proc/13481
- MathSciNet review: 3652801