A Lie bialgebra is a structure that arises in the study of mathematical physics and the theory of quantum groups. It combines the concepts of Lie algebras and coalgebras.
A **Lie algebra** is a vector space \( \mathfrak{g} \) equipped with a binary operation called the Lie bracket, denoted \( [ \cdot , \cdot ] \), which is bilinear, skew-symmetric, and satisfies the Jacobi identity.
A **coalgebra** is a vector space \( C \) equipped with two


