The primality of subfactors of finite index

in the interpolated free group factors

Author:
Marius B. Stefan

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that any II-subfactor of finite index in the interpolated free group factor is prime for any i.e., it is not isomorphic to tensor products of II-factors.

**[1]**Dykema, K.,*Interpolated free group factors*, Pac. J. Math.**163**(1994), 123-135. MR**95c:46103****[2]**Dykema, K.,*Two applications of free entropy*, Math. Ann.**308**(1997), 547-558. CMP**97:15****[3]**Ge, L.,*Applications of free entropy to finite von Neumann algebras, II*, Preprint.**[4]**Ge, L.,*Prime Factors*, Proc. Nat. Acad. Sci. (USA)**93**(1996), 12762-12763. CMP**97:03****[5]**Haagerup, U.,*An Example of a Non Nuclear -Algebra which has the Metric Approximation Property*, Invent. Math.**50**(1979), 279-293. MR**80j:46094****[6]**Jones, V.F.R.,*Index for Subfactors*, Invent. Math.**72**(1983), 1-25. MR**84d:46097****[7]**Popa, S.,*Orthogonal pairs of -subalgebras in finite von Neumann algebras*, J. Op. Theory**9**(1983), 253-268. MR**84h:46077****[8]**Popa, S.,*Free-independent sequences in type II factors and related problems*, Astérisque**232**(1995), 187-202. MR**97b:46080****[9]**R\u{a}dulescu, F.,*Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index*, Invent. Math.**115**(1994), 347-389. MR**95c:46102****[10]**Szarek, S.J.,*Nets of Grassmann manifolds and orthogonal group*, Proceedings of Research Workshop on Banach Space Theory (Bor-Luh-Lin, ed.), The University of Iowa, June 29-31 (1982), 169-185. MR**85h:58021****[11]**Voiculescu, D.,*Circular and semicircular systems and free product factors. Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory*, Progress in Mathematics**92**(1990), 45-60. MR**92e:46124****[12]**Voiculescu, D.,*The analogues of entropy and of Fisher's information measure in free probability theory, II*, Invent. Math.**118**(1994), 411-440. MR**96a:46117****[13]**Voiculescu, D.,*The analogues of entropy and of Fisher's information measure in free probability theory III: the absence of Cartan subalgebras*, G.A.F.A.**6, No. 1**(1996), 172-199. MR**96m:46119**

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Additional Information

**Marius B. Stefan**

Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Email:
stefan@math.uiowa.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04309-3

Keywords:
Free entropy,
prime factors

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

Article copyright:
© Copyright 1998
American Mathematical Society