The primality of subfactors of finite index in the interpolated free group factors

Ştefan, Marius

doi:10.1090/S0002-9939-98-04309-3

The primality of subfactors of finite index in the interpolated free group factors
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by Marius B. Ştefan PDF

Proc. Amer. Math. Soc. 126 (1998), 2299-2307 Request permission

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