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 Jacques Tits (1962), Kantor (1964), and Koecher (1967). 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.

Source: Wikipedia — Kantor–Koecher–Tits construction (CC BY-SA 4.0)