A Class of Homeomorphisms on Homogeneous Spaces of a Group Action
Functional Analysis
2023-08-22 v1 Representation Theory
Abstract
We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a locally convex topological vector space which is also convex must necessarily be trivial, ie. a singleton set. Additionally, this class of homeomorphisms allows us to relate the induced group action on the space of continuous functions to the action on the homogeneous space.
Keywords
Cite
@article{arxiv.2308.09799,
title = {A Class of Homeomorphisms on Homogeneous Spaces of a Group Action},
author = {Samuel A. Hokamp},
journal= {arXiv preprint arXiv:2308.09799},
year = {2023}
}