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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
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2023
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| 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.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2023-04-17
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0431068
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2023-05
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International