Crossed products of $\textrm {II}_ 1$-subfactors by strongly outer actions
HTML articles powered by AMS MathViewer
- by Carl Winsløw PDF
- Trans. Amer. Math. Soc. 347 (1995), 985-991 Request permission
Abstract:
We study the crossed product $A \rtimes G \supseteq B \rtimes G$ of an inclusion $A \supseteq B$ of type ${\text {I}}{{\text {I}}_1}$-factors by a discrete strongly outer action $G$. In particular, we find conditions under which the strong amenability of $A \supseteq B$ implies that of $A \rtimes G \supseteq B \rtimes G$, and vice versa.References
- P.-L. Aubert, Théorie de Galois pour une $W^*$-algèbre, Comment. Math. Helv. 51 (1976), no. 3, 411–433. MR 428055, DOI 10.1007/BF02568166
- Marie Choda and Hideki Kosaki, Strongly outer actions for an inclusion of factors, J. Funct. Anal. 122 (1994), no. 2, 315–332. MR 1276161, DOI 10.1006/jfan.1994.1071
- A. Connes, Classification of injective factors. Cases $II_{1},$ $II_{\infty },$ $III_{\lambda },$ $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 454659, DOI 10.2307/1971057
- Fumio Hiai, Minimizing indices of conditional expectations onto a subfactor, Publ. Res. Inst. Math. Sci. 24 (1988), no. 4, 673–678. MR 976765, DOI 10.2977/prims/1195174872
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127 V. F. R. Jones and S. Popa, Some properties of MASA ’s in factors, Proc. 6th Internat. Conf. on Operator Theory, Birkhäuser, Boston, 1982.
- Phan H. Loi, On automorphisms of subfactors, J. Funct. Anal. 141 (1996), no. 2, 275–293. MR 1418506, DOI 10.1006/jfan.1996.0128 —, On the derived tower of certain inclusions of type ${\text {II}}{{\text {I}}_\lambda }$ factors of index $4$, Pacific J. Math. (to appear).
- Roberto Longo, Minimal index and braided subfactors, J. Funct. Anal. 109 (1992), no. 1, 98–112. MR 1183606, DOI 10.1016/0022-1236(92)90013-9
- Adrian Ocneanu, Actions of discrete amenable groups on von Neumann algebras, Lecture Notes in Mathematics, vol. 1138, Springer-Verlag, Berlin, 1985. MR 807949, DOI 10.1007/BFb0098579
- Sorin Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), no. 2, 163–255. MR 1278111, DOI 10.1007/BF02392646 —, Classification of actions of discrete amenable groups on amenable subfactors of type II, preprint, 1992.
- Carl Winsløw, Strongly free actions on subfactors, Internat. J. Math. 4 (1993), no. 4, 675–688. MR 1232987, DOI 10.1142/S0129167X93000327
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 985-991
- MSC: Primary 46L35; Secondary 46L37, 46L40
- DOI: https://doi.org/10.1090/S0002-9947-1995-1242110-8
- MathSciNet review: 1242110