What question did this study set out to answer?

The research aims to explore the properties of normalizers and centralizers in Lie groups and their implications for operator semistable measures.

March 29, 2026Open Access

Normalizers of Compact Subgroups, the Existence of Commuting Automophisms, and Applications to Operator Semistable Measures

Key Points

The research aims to explore the properties of normalizers and centralizers in Lie groups and their implications for operator semistable measures.
Analyzed the structure of Lie groups and compact subgroups.
Investigated the properties of normalizers and centralizers within this mathematical framework.
Applied the findings to characterize operator semistable measures.
Established that the normalizer and centralizer of compact subgroups are finite.
Clarified the implications of these results for theoretical probability concerning operator semistable measures.

Abstract

Let G be a Lie group with finitely many components and K a compact subgroup with identity component K 0 .The normalizer, respectively, centralizer ofis 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.

Bookmark

View Full Paper