Reduction of structure to parabolic subgroups
Copyright policy )Reduction of structure to parabolic subgroups
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.
torsors, Bilinear and Hermitian forms, isotropy, Galois cohomology of linear algebraic groups, Galois cohomology, anisotropy, Mathematics - Rings and Algebras, Group Theory (math.GR), parabolic subgroups, Linear algebraic groups over arbitrary fields, Mathematics - Algebraic Geometry, 11E72, 20G15, 20G07 (Primary), 11E39, 16W10 (Secondary), Rings and Algebras (math.RA), Structure theory for linear algebraic groups, Rings with involution; Lie, Jordan and other nonassociative structures, FOS: Mathematics, Mathematics - Group Theory, Algebraic Geometry (math.AG), linear algebraic groups
torsors, Bilinear and Hermitian forms, isotropy, Galois cohomology of linear algebraic groups, Galois cohomology, anisotropy, Mathematics - Rings and Algebras, Group Theory (math.GR), parabolic subgroups, Linear algebraic groups over arbitrary fields, Mathematics - Algebraic Geometry, 11E72, 20G15, 20G07 (Primary), 11E39, 16W10 (Secondary), Rings and Algebras (math.RA), Structure theory for linear algebraic groups, Rings with involution; Lie, Jordan and other nonassociative structures, FOS: Mathematics, Mathematics - Group Theory, Algebraic Geometry (math.AG), linear algebraic groups
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