Linear Dynamical Systems of Nilpotent Lie Groups

We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular poi...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2021-10, Vol.27 (5), Article 74
Main Authors: Beltita, Ingrid, Beltita, Daniel
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Algebra
Approximations and Expansions
Dynamical systems
Fourier Analysis
Group theory
Lie groups
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Orbits
Partial Differential Equations
Representations
Signal,Image and Speech Processing
Topology
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Summary:We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular points is dense, and then the interior of that complement is either empty or dense in the representation space. The regular points are by definition the points whose orbits are locally compact in their relative topology. We thus generalize some results from the recent literature on linear actions of abelian Lie groups. As an application, we determine the generalized a x + b -groups whose C ∗ -algebras are antiliminary, that is, no closed 2-sided ideal is type I.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-021-09882-7