Non-measurable automorphisms of Lie groups relative to the real- and non-archimedean-valued measures

TL;DR

This paper investigates the existence and construction of non-measurable automorphisms of finite and infinite-dimensional Lie groups over real and non-archimedean fields, and explores their applications in representation theory.

Contribution

It proves the existence of non-measurable automorphisms and provides a method for constructing them, extending the understanding of measure theory in Lie groups.

Findings

Existence of non-measurable automorphisms in Lie groups over various fields

Construction procedure for non-measurable automorphisms

Application to non-measurable irreducible unitary representations

Abstract

In this work the problem about an existence of non-measurable automorphisms of Lie groups finite and as well infinite dimensional over the field of real numbers and also over the non-archimedean local fields is investigated. Non-measurability of automorphisms is considered relative to real-valued measures and also measures with values in non-archimedean local fields. Their existence is proved and a procedure for their construction is given. Their application for a construction of non-measurable irreducible unitary representations is demonstrated.