Lie coalgebra

Summary

A Lie coalgebra is the dual notion of a Lie algebra. It is a vector space with a cobracket that sends each element to an antisymmetric tensor of order two. The cobracket satisfies a dual form of the Jacobi identity. The dual space of a finite-dimensional Lie algebra is a Lie coalgebra, and every finite-dimensional Lie coalgebra arises in this way. Lie coalgebras appear in rational homotopy theory and as one half of a Lie bialgebra.