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About: Kantor–Koecher–Tits construction     Goto   Sponge   NotDistinct   Permalink

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In algebra, the Kantor–Koecher–Tits construction is a method of constructing a Lie algebra from a Jordan algebra, introduced by Jacques Tits, Kantor, and Koecher. If J is a Jordan algebra, the Kantor–Koecher–Tits construction puts a Lie algebra structure on J + J + Inner(J), the sum of 2 copies of J and the Lie algebra of inner derivations of J. When applied to a 27-dimensional exceptional Jordan algebra it gives a Lie algebra of type E7 of dimension 133. The Kantor–Koecher–Tits construction was used by to classify the finite-dimensional simple Jordan superalgebras.