Kantor–Koecher–Tits construction
In algebra, the Kantor–Koecher–Tits construction is a method of constructing a Lie algebra from a Jordan algebra, introduced by , , and . 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. References

Lie algebras
Non-associative algebras