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Imbedding of Lie triple systems into Lie algebras
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math.RAmath.DG
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algebrascategorygradedsystemstriplealgberaanalogouscoefficients
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We show that the category of Lie triple systems is equivalent to the category of Lie algebras graded by Z/(2Z) such that the odd component generates the algbera and the second graded cohomology group coefficients in any trivial module is zero. As a corollary we obtain an analogous result for symmetric spaces and Lie groups.
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