Tits–Kantor–Koecher Lie algebras of JB*-triples

摘要

We characterise the Tits–Kantor–Koecher Lie algebra of a JB*-triple which can be infinite dimensional. In particular, we show that a complex Lie algebra is the Tits–Kantor–Koecher Lie algebra of a JB*-triple if and only if it has a real form which is isomorphic to the reduced Lie algebra of a bounded symmetric domain. Matrix representations of these Lie algebras are also presented.