In mathematics, a Manin triple consists of a Lie algebra with a non-degenerate invariant symmetric bilinear form, together with two isotropic subalgebras and such that is the direct sum of and 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 Vladimir Drinfeld in 1987, who named them after Yuri Manin.[1]
In 2001 Delorme classified Manin triples where is a complex reductive Lie algebra.[2]