Adjoint Vector Fields on the Tangent Space of Semisimple Symmetric Spaces
نویسنده
چکیده
Let g be a semisimple complex Lie algebra and θ ∈ Aut g be an involution. If g = k⊕ p is the decomposition associated to θ , define a Lie subalgebra of End p by k̃ = {X : ∀f ∈ S(p∗)k, X.f = 0} . We prove that adp(k) = k̃ if, and only if, each irreducible factor of rank one of the symmetric pair (g, k) is isomorphic to (so(q + 1), so(q)) .
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تاریخ انتشار 1999