Journal of Lie Theory
Vol. 8, No. 2, pp. 189-209 (1998)

Normalizers of compact subgroups, the existence of commuting automorphisms, and applications to operator semistable measures

W. Hazod, K. H. Hofmann, H.-P. Scheffler, M. Wüstner, and H. Zeuner

W.Hazod and H.-P.Scheffler
Institut für Mathematik
Universität Dortmund
Campus Nord, Mathematikgebäude
D-44221 Dortmund, Germany

K.H.Hofmann and M.Wüstner
Fachbereich Mathematik
Technische Universität Darmstadt
Schlossgartenstr. 7
D-64289 Darmstadt, Germany

Medizinische Universität zu Lübeck
Technisch-Naturwissenschaftliche Fakultät
Wallstr. 40
D-23560 Lübeck, Germany

Abstract: Let $\scriptstyle G$ be a Lie group with finitely many components and $\scriptstyle K$ a compact subgroup with identity component $\scriptstyle K_0$. The normalizer, respectively, centralizer of $\scriptstyle K$ in $\scriptstyle G$ is denoted by $\scriptstyle N(K,G)$, respectively, $\scriptstyle Z(K,G)$. It is shown that $\scriptstyle N(K,G)/K_0Z(K,G)$ is finite. This is applied to a problem in theoretical probability theory, namely, to the characterisation of operator semistable measures. The article explains these concepts and puts the present application into perspective.

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