A Kurosh-type theorem for type III factors
HTML articles powered by AMS MathViewer
- by Jason Asher
- Proc. Amer. Math. Soc. 137 (2009), 4109-4116
- DOI: https://doi.org/10.1090/S0002-9939-09-10009-6
- Published electronically: July 20, 2009
- PDF | Request permission
Abstract:
We prove a generalization of N. Ozawaโs Kurosh-type theorem to the setting of free products of semiexact $\text {II}_1$ factors with respect to arbitrary (non-tracial) faithful normal states. We are thus able to distinguish certain resulting type III factors. For example, if $M = LF_n \otimes LF_m$ and $\{\varphi _i\}$ is any sequence of faithful normal states on $M$, then the $l$-various $(M,\varphi _1) * ... * (M,\varphi _l)$ are all mutually non-isomorphic.References
- I. Chifan and C. Houdayer, Prime factors and amalgamated free products. Preprint (2008). arXiv:0805.1566
- Mingchu Gao and Marius Junge, Examples of prime von Neumann algebras, Int. Math. Res. Not. IMRN 15 (2007), Art. ID rnm042, 34. MR 2348404, DOI 10.1093/imrn/rnm042
- Narutaka Ozawa, A Kurosh-type theorem for type $\rm II_1$ factors, Int. Math. Res. Not. , posted on (2006), Art. ID 97560, 21. MR 2211141, DOI 10.1155/IMRN/2006/97560
- Narutaka Ozawa, Solid von Neumann algebras, Acta Math. 192 (2004), no.ย 1, 111โ117. MR 2079600, DOI 10.1007/BF02441087
- Narutaka Ozawa and Sorin Popa, Some prime factorization results for type $\textrm {II}_1$ factors, Invent. Math. 156 (2004), no.ย 2, 223โ234. MR 2052608, DOI 10.1007/s00222-003-0338-z
- Sorin Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), no.ย 2, 163โ255. MR 1278111, DOI 10.1007/BF02392646
- Sorin Popa, Orthogonal pairs of $\ast$-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), no.ย 2, 253โ268. MR 703810
- Sorin Popa, Strong rigidity of $\rm II_1$ factors arising from malleable actions of $w$-rigid groups. I, Invent. Math. 165 (2006), no.ย 2, 369โ408. MR 2231961, DOI 10.1007/s00222-006-0501-4
- Dimitri Shlyakhtenko, Prime type III factors, Proc. Natl. Acad. Sci. USA 97 (2000), no.ย 23, 12439โ12441. MR 1791311, DOI 10.1073/pnas.220417397
- M. Takesaki, Theory of operator algebras. II, Encyclopaedia of Mathematical Sciences, vol. 125, Springer-Verlag, Berlin, 2003. Operator Algebras and Non-commutative Geometry, 6. MR 1943006, DOI 10.1007/978-3-662-10451-4
- Stefaan Vaes and Roland Vergnioux, The boundary of universal discrete quantum groups, exactness, and factoriality, Duke Math. J. 140 (2007), no.ย 1, 35โ84. MR 2355067, DOI 10.1215/S0012-7094-07-14012-2
- Dan Voiculescu, Symmetries of some reduced free product $C^\ast$-algebras, Operator algebras and their connections with topology and ergodic theory (Buลteni, 1983) Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp.ย 556โ588. MR 799593, DOI 10.1007/BFb0074909
Bibliographic Information
- Jason Asher
- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
- Email: asherj@math.ucla.edu
- Received by editor(s): November 13, 2008
- Received by editor(s) in revised form: March 8, 2009
- Published electronically: July 20, 2009
- Additional Notes: Research supported in part by NSF grant DMS-0555680 and NSF VIGRE grant DMS-0701302.
- Communicated by: Marius Junge
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4109-4116
- MSC (2000): Primary 46L10, 46L09
- DOI: https://doi.org/10.1090/S0002-9939-09-10009-6
- MathSciNet review: 2538572