The primality of subfactors of finite index in the interpolated free group factors
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- by Marius B. Ştefan
- Proc. Amer. Math. Soc. 126 (1998), 2299-2307
- DOI: https://doi.org/10.1090/S0002-9939-98-04309-3
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Abstract:
In this paper we prove that any II$_{1}$-subfactor of finite index in the interpolated free group factor $L(F_{t})$ is prime for any $1<t\leq \infty$ i.e., it is not isomorphic to tensor products of II$_{1}$-factors.References
- Ken Dykema, Interpolated free group factors, Pacific J. Math. 163 (1994), no. 1, 123–135. MR 1256179, DOI 10.2140/pjm.1994.163.123
- Dykema, K., Two applications of free entropy, Math. Ann. 308 (1997), 547–558.
- Ge, L., Applications of free entropy to finite von Neumann algebras, II, Preprint.
- Ge, L., Prime Factors, Proc. Nat. Acad. Sci. (USA) 93 (1996), 12762–12763.
- Uffe Haagerup, An example of a nonnuclear $C^{\ast }$-algebra, which has the metric approximation property, Invent. Math. 50 (1978/79), no. 3, 279–293. MR 520930, DOI 10.1007/BF01410082
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
- Sorin Popa, Orthogonal pairs of $\ast$-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), no. 2, 253–268. MR 703810
- Sorin Popa, Free-independent sequences in type $\textrm {II}_1$ factors and related problems, Astérisque 232 (1995), 187–202. Recent advances in operator algebras (Orléans, 1992). MR 1372533
- Florin Rădulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index, Invent. Math. 115 (1994), no. 2, 347–389. MR 1258909, DOI 10.1007/BF01231764
- Stanisław J. Szarek, Nets of Grassmann manifold and orthogonal group, Proceedings of research workshop on Banach space theory (Iowa City, Iowa, 1981) Univ. Iowa, Iowa City, IA, 1982, pp. 169–185. MR 724113
- Dan Voiculescu, Circular and semicircular systems and free product factors, Operator algebras, unitary representations, enveloping algebras, and invariant theory (Paris, 1989) Progr. Math., vol. 92, Birkhäuser Boston, Boston, MA, 1990, pp. 45–60. MR 1103585
- Dan Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory. II, Invent. Math. 118 (1994), no. 3, 411–440. MR 1296352, DOI 10.1007/BF01231539
- D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory. III. The absence of Cartan subalgebras, Geom. Funct. Anal. 6 (1996), no. 1, 172–199. MR 1371236, DOI 10.1007/BF02246772
Bibliographic Information
- Marius B. Ştefan
- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
- Email: stefan@math.uiowa.edu
- Received by editor(s): November 27, 1996
- Received by editor(s) in revised form: January 10, 1997
- Additional Notes: The author is a member of the Institute of Mathematics, Romanian Academy, Bucharest
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2299-2307
- MSC (1991): Primary 46L37, 46L50; Secondary 22D25
- DOI: https://doi.org/10.1090/S0002-9939-98-04309-3
- MathSciNet review: 1443410