Jones' Index For Fixed Point Algebras
Commun. Korean Math. Soc. 1998 Vol. 13, No. 1, 29-36
Jung Rye Lee
Daejin University
Abstract : We show that if $M$ is a II${}_1$-factor and a countable discrete group $G$ acts outerly on $M$ then Jones' index $[M:M^{G}]$ of a pair of II${}_1$-factors is equal to the order $|G|$ of $G$. It is also shown that for a subgroup $H$ of $G$ Jones' index $[M^{H}:M^{G}]$ is equal to the group index $[G:H]$ under certain conditions.
Keywords : Jones' index, fixed point algebra, group von Neumann algebra
MSC numbers : 46L55
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