2008/09/16 by Caroline B. Wright, Wright, Caroline B.
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #06B15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:06B15
paper · pdf · doi:10.48550/arxiv.0809.2833
49 pages, 4 appendices, 6 tables
openalex publication_date 2008/09/16 · arxiv created 2010/10/23 · arxiv updated 2010/10/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Let G be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic p > 0. Let T be a maximal split torus in G, B ⊃ T be a Borel subgroup of G and U its unipotent radical. Let F: G → G be the Frobenius morphism. For r ≥ 1 define the Frobenius kernel, Gr, to be the kernel of F iterated with itself r times. Define Ur (respectively Br) to be the kernel of the Frobenius map restricted to U (respectively B). Let X(T) be the integral weight lattice and X(T)+ be the dominant integral weights. The computations of particular importance are \h2(U1,k), \h2(Br,\la) for \la ∈ X(T), \h2(Gr,H0(\la)) for \la ∈ X(T)+, and \h2(B,\la) for \la ∈ X(T). The above cohomology groups for the case when the field has characteristic 2 one computed in this paper. These computations complete the picture started by Bendel, Nakano, and Pillen for p ≥ 3 \citeBNP2.