Abstract
In a recent paper ([14]) the second author showed that if N is a subfactor of a finite factor M with trivial relative commutant, one may find a MASA (maximal abelian *-subalgebra) A in N which is also MASA in M. It was also possible to control certain unitaries normalizing A and this led to some further questions. In this paper we give some answers to these questions.
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References
Aubert, P.L.: Théorie de Galois pour une W*-algèbre, Comment. Math. Helvetici, 39(51) (1976), 411–433.
Connes, A.: Classification of injective factors, Ann. of Math., 104 (1976), 73–115.
Connes, A.; Jones, V.: A II1 factor with two nonconjugate Cartan subalgebras, Bull. Amer. Math. Soc., to appear.
Connes, A.; Feldmann, J.; Weiss, B.: Amenable equivalence relations are generated by a single transformation, preprint.
Dixmier, J.: Sous-anneaux abéliens maximaux dans les facteurs de type fini, Ann. of Math. 59 (1954), 279–286.
Dye, H.: On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551–576.
Feldmann, J.; Moore, C.C.: Ergodic equivalence relations, cohomology and von Neumann algebras. II, Trans. Amer. Math. Soc. 234 (1977), 325–361.
Haga, Y.; Takeda, Z.: Correspondence between subgroups and subalgebras in a cross product von Neumann algebra, Tôhoku Math. J. 24 (1972), 167–190.
Jones, V.: Sur la conjugaison des sous-facteurs de type II1 C.R. Acad. Sci. Paris, Sér. A 284 (1977), 597–598.
Jones, V.: Actions of finite groups on the hyperfinite type II 1 factor, Memoirs A.M.S., no.237, 1980.
Mc Duff, D.: Central sequences and the hyperfinite factor, Proc. London Math. Soc. 21 (1970), 443–461.
Ocneanu, A.: Actions des groupes moyennables sur les algèbres de von Neumann, C.R. Acad. Sci. Paris, Sér. A, 1980.
Paschke, W.L.: Inner product modules arising from compact automorphisms groups of von Neumann algebras, Trans. Amer. Math. Soc. 224 (1976), 87–102.
Popa, S.: On a problem of R.V. Kadison on maximal abelian *-subalgebras in. factors, Invent. Math. 65 (1981), 269–281.
Popa, S.: On MASA’s of algebras associated with free groups, INCREST preprint, no.40/1981.
Popa, S.: Orthogonal pairs of subalgebras in finite factors, INCREST preprint, no. 89 (1981).
Sakai, S.: C*-algebras and W*-algebras, Springer Verlag, 1971.
Strătilă, S.: Modular theory, Editura Academiei and Abacus Press, 1981.
Tauer, R.F.: Maximal abelian subalgebras in finite factors, Trans. Amer. Math.Soc. 114 (1965), 281–308.
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Jones, V.R.F., Popa, S. (1982). Some Properties of Masa’s in Factors. In: Apostol, C., Douglas, R.G., Sz.-Nagy, B., Voiculescu, D., Arsene, G. (eds) Invariant Subspaces and Other Topics. Operator Theory: Advances and Applications, vol 6. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5445-0_8
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DOI: https://doi.org/10.1007/978-3-0348-5445-0_8
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