Date of Award:
12-2026
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Peter Crooks
Committee
Peter Crooks
Committee
Matthew Young
Committee
David Brown
Abstract
Let G be a complex semisimple linear algebraic group with 𝐶 a conjugacy class of parabolic subgroups of G. In previous work, Dr. Crooks defines 𝑢𝐶→ B𝐶 , a universal flat family of a fine Hamiltonian Lagrangian G-bundles over 𝐶, and shows that 𝑢𝐶 is a family of regular Poisson varieties. This manuscript introduces a natural candidate for a quasi-Poisson analog of Dr. Crooks’s construction, 𝑢𝐶, using the framework of quasi-Poisson geometry established by Alekseev, Kosmann-Scwarzbach, and Meinrenken. It will be shown that this proposed quasi-Poisson analog indeed has a valid quasi-Poisson structure and is a family of regular quasi-Poisson varieties.
Recommended Citation
Thompson, Casen, "Quasi-Poisson Analogs of Regular Poisson Varieties" (2026). All Graduate Theses and Dissertations, Fall 2023 to Present. 939.
https://digitalcommons.usu.edu/etd2023/939
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