A Lie bialgebroid is a mathematical structure in the area of non-Riemannian differential geometry. Wikipedia

A pair of two compatible Lie algebroids defined on dual vector bundles; here Lie algebroid is a vector bundle with a map into the tangent bundle over its base manifold and an anticommutative bracket operation on the space of sections of the vector bundle satisfying some axioms Wikipedia Disambiguation

Pair of two compatible Lie algebroids defined on dual vector bundles Wikidata