Manin triple

In mathematics, a Manin triple (g, p, q) consists of a Lie algebra g with a non-degenerate invariant symmetric bilinear form, together with two isotropic subalgebras p and q such that g is the direct sum of p and q as a vector space. A closely related concept is the (classical) Drinfeld double, which is an even dimensional Lie algebra which admits a Manin decomposition.

Manin triples were introduced by Drinfeld (1987, p.802), who named them after Yuri Manin.

Delorme (2001) classified the Manin triples where g is a complex reductive Lie algebra.