Real Elements in Spin Groups
نویسنده
چکیده
Let F be a field of characteristic 6= 2. Let G be an algebraic group defined over F . An element t ∈ G(F ) is called real if there exists s ∈ G(F ) such that sts = t. A semisimple element t in GLn(F ), SLn(F ), O(q), SO(q), Sp(2n) and the groups of type G2 over F is real if and only if t = τ1τ2 where τ 2 1 = ±1 = τ 2 2 (ref. [ST1, ST2]). In this paper we extend this result to the semisimple elements in Spin groups when dim(V ) ≡ 0, 1, 2 (mod 4).
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