Crossed products of 𝐼𝐼₁-subfactors by strongly outer actions

Winsløw, Carl

doi:10.1090/S0002-9947-1995-1242110-8

Crossed products of $\textrm {II}_ 1$-subfactors by strongly outer actions
HTML articles powered by AMS MathViewer

by Carl Winsløw

Trans. Amer. Math. Soc. 347 (1995), 985-991

DOI: https://doi.org/10.1090/S0002-9947-1995-1242110-8

PDF | 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

Some properties of MASA ’s in factors

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

factors of index

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

Carl Winsløw, Strongly free actions on subfactors, Internat. J. Math. 4 (1993), no. 4, 675–688. MR 1232987, DOI 10.1142/S0129167X93000327