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Reduction of structure to parabolic subgroups Ofek, Danny

Abstract

Let G be an affine group over a field of characteristic not two. A G-torsor is called isotropic if it admits reduction of structure to a proper parabolic subgroup of G. This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does G admit anisotropic torsors? Building on work of J. Tits, we answer this question for simple groups. We also give an answer for connected and semisimple G under certain restrictions on its root system.

Item Metadata

Title
Reduction of structure to parabolic subgroups
Creator
Ofek, Danny
Supervisor
Reichstein, Zinovy
Publisher
University of British Columbia
Date Issued
2023
Description
Let G be an affine group over a field of characteristic not two. A G-torsor is called isotropic if it admits reduction of structure to a proper parabolic subgroup of G. This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does G admit anisotropic torsors? Building on work of J. Tits, we answer this question for simple groups. We also give an answer for connected and semisimple G under certain restrictions on its root system.
Genre
Thesis/Dissertation
Type
Text
Language
eng
Date Available
2023-04-17
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0431068
URI
http://hdl.handle.net/2429/84223
Degree (Theses)
Master of Science - MSc
Program (Theses)
Mathematics
Affiliation
Science, Faculty of; Mathematics, Department of
Degree Grantor
University of British Columbia
Graduation Date
2023-05
Campus
UBCV
Scholarly Level
Graduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International