## Duke Mathematical Journal

### On some decomposition properties for factors of type $\mathrm{II}_1$

#### Article information

Source
Duke Math. J., Volume 94, Number 1 (1998), 79-101.

Dates
First available in Project Euclid: 19 February 2004

https://projecteuclid.org/euclid.dmj/1077230078

Digital Object Identifier
doi:10.1215/S0012-7094-98-09405-4

Mathematical Reviews number (MathSciNet)
MR1635904

Zentralblatt MATH identifier
0947.46042

Subjects
Primary: 46L35: Classifications of $C^*$-algebras

#### Citation

Ge, Liming; Popa, Sorin. On some decomposition properties for factors of type $\mathrm{II}_1$. Duke Math. J. 94 (1998), no. 1, 79--101. doi:10.1215/S0012-7094-98-09405-4. https://projecteuclid.org/euclid.dmj/1077230078

#### References

• [BH] E. Bédos and P. de la Harpe, Moyennabilité intérieure des groupes: définitions et exemples, Enseign. Math. (2) 32 (1986), no. 1-2, 139–157.
• [Ch] M. Choda, Outer actions of groups with property $T$ on the hyperfinite $\mathrm{II}_1$-factor, Math. Japan. 31 (1986), no. 4, 533–551.
• [CES] E. Christensen, E. Effros, and A. Sinclair, Completely bounded multilinear maps and $C^ \ast$-algebraic cohomology, Invent. Math. 90 (1987), no. 2, 279–296.
• [CS] E. Christensen and A. Sinclair, On the Hochschild cohomology for von Neumann algebras, preprint.
• [C1] A. Connes, Classification of injective factors. Cases $II\sb{1},$ $II\sb{\infty },$ $III\sb{\lambda },$ $\lambda \not=1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115.
• [C2] A. Connes, Classification des facteurs, Operator Algebras and Applications, Part 2 (Kingston, Ont., 1980), Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, 1982, pp. 43–109.
• [CJ] A. Connes and V. Jones, Property $T$ for von Neumann algebras, Bull. London Math. Soc. 17 (1985), no. 1, 57–62.
• [D] J. Dixmier, Quelques propriétés des suites centrales dans les facteurs de type ${\rm II}\sb{1}$, Invent. Math. 7 (1969), 215–225.
• [FM1] J. Feldman and C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc. 234 (1977), no. 2, 289–324.
• [FM2] J. Feldman and C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, II, Trans. Amer. Math. Soc. 234 (1977), no. 2, 325–359.
• [Ge1] L. Ge, Applications of free entropy to finite von Neumann algebras, Amer. J. Math. 119 (1997), no. 2, 467–485.
• [Ge2] L. Ge, Applications of free entropy to finite von Neumann algebras, II, to appear in Ann. of Math. (2).
• [H] U. Haagerup, An example of a nonnuclear $C^{\ast}$-algebra, which has the metric approximation property, Invent. Math. 50 (1978/79), no. 3, 279–293.
• [JKR] B. Johnson, R. Kadison, and J. Ringrose, Cohomology of operator algebras, III: Reduction to normal cohomology, Bull. Soc. Math. France 100 (1972), 73–96.
• [K1] R. Kadison, Derivations of operator algebras, Ann. of Math. (2) 83 (1966), 280–293.
• [K2] R. Kadison, Problems on von Neumann algebras, paper given at the Conference on Operator Algebras and Their Applications, Louisiana State University, Baton Rouge, La., 1967.
• [KR] R. Kadison and J. Ringrose, Cohomology of operator algebras, I: Type $I$ von Neumann algebras, Acta Math. 126 (1971), 227–243.
• [MvN1] F. Murray and J. von Neumann, On rings of operators, Ann. of Math.(2) 37 (1936), 116–229.
• [MvN2] F. Murray and J. von Neumann, On rings of operators, IV, Ann. of Math. (2) 44 (1943), 716–808.
• [Pe] C. Pearcy, On certain von Neumann algebras which are generated by partial isometries, Proc. Amer. Math. Soc. 15 (1964), 393–395.
• [PSm] F. Pop and R. Smith, Cohomology for certain finite factors, Bull. London Math. Soc. 26 (1994), no. 3, 303–308.
• [Po1] S. Popa, On a problem of R. V. Kadison on maximal abelian $\ast$-subalgebras in factors, Invent. Math. 65 (1981/82), no. 2, 269–281.
• [Po2] S. Popa, Singular maximal abelian $\ast$-subalgebras in continuous von Neumann algebras, J. Funct. Anal. 50 (1983), no. 2, 151–166.
• [Po3] S. Popa, Correspondences, preprint, 1986.
• [Po4] S. Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), no. 2, 163–255.
• [Po5] S. Popa, Symmetric enveloping algebras, amenability and AFD properties for subfactors, Math. Res. Lett. 1 (1994), no. 4, 409–425.
• [Po6] S. Popa, Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property $T$, preprint, 1997.
• [Sz] S. 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.
• [V1] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent. Math. 118 (1994), no. 3, 411–440.
• [V2] 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.
• [W] W. Wogen, On generators for von Neumann algebras, Bull. Amer. Math. Soc. 75 (1969), 95–99.