Work

A Peter–Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions

Year: 2026

Type: article

Abstract: We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundle of compact homogeneous spaces. Our result holds without restrictions on the acting group or the underlying probability spaces. This generalizes previous work by Mackey, Zimmer, Ellis, Austin, and the second author and Tao, and is inspired by the Furstenberg–Zimmer and Host–Kra structure theories for actions of uncountable groups. Our approach uses a natural model to answer the ergodic-theoretic question with the help of structure theory for topological dynamical systems. A key step in our argument is establishing a Peter–Weyl-type theorem for bundles of compact groups which might be of independent interest.

Source: Documenta Mathematica

DOI: 10.4171/dm/1093

Authors: Nikolai Edeko, Asgar Jamneshan, Henrik Kreidler

Institutions: University of Zurich, University of Bonn, University of Wuppertal, Leipzig University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4322717222

FWCI:

Cites:

Cited by:

Related to: 10