Title: Orthogonal groups containing a given maximal torus
Abstract: Let k be a field of characteristic different from 2 and let T be a fixed k-torus of dimension n. In this paper we study faithful k-representations ρ:T→SO(A,σ), where (A,σ) is a central simple algebra of degree 2n with orthogonal involution σ. Note that in this case ρ(T) is a maximal torus in SO(A,σ). We are interested in describing the pairs (A,σ) for which there is such a representation. We compute invariants for these algebras (discriminant and Clifford algebra), which are sufficient to determine their isomorphism class when I3(k)=0 by a theorem of Lewis and Tignol. The first part of the paper is devoted to the case where A is split over k and an application to a theorem of Feit on orthogonal groups over Q is given.
Publication Year: 2003
Publication Date: 2003-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 22
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