Cohomology of algebraic groups
نویسندگان
چکیده
منابع مشابه
Detecting Rational Cohomology of Algebraic Groups
Let G be a connected, semisimple algebraic group defined over an algebraically closed field k of positive characteristic p. Assume that G is defined and split over the prime field k0 = GF (p), and for q = p , let G(q) be the subgroup of GF (g)-rational points. Let V be a rational G-module, and, for a non-negative integer r, let V(r) be the rational G-module obtained by 'twisting' the original G...
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LetG be a quasisimple, connected, and simply connected algebraic group defined and split over the field k of characteristic p > 0. In this paper, we are interested in small modules for G; for us, small modules are those with dimension ≤ p. By results of Jantzen [Jan96] one knows that anyGmodule V with dimV ≤ p is semisimple. (We always understand aG-module V to be given by a morphism of algebra...
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for nonnegative integers nβα. Each root β corresponds to a unipotent subgroup Uβ of G, whose Lie algebra is gβ. There is an isomorphism of the additive Lie groupGa ∼= C with Uβ; this is T -equivariant, with multiplication by β(t) on C corresponding to conjugation by t on Uβ (u 7→ tut −1). The product of the groups Uβ for β ∈ R+ forms a unipotent group U , isomorphic to C , with N = #R+, and B =...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90087-7