Lie algebras

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 , who named them after Yuri Manin. classified the Manin triples where g is a complex reductive Lie algebra. (Wikipedia).

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Related pages

Lie bialgebra | Symmetric bilinear form | Reductive Lie algebra | Borel subalgebra | Lie algebra