Coassociative Lie algebras

A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the usual universal enveloping algebra of a Lie algebra. This new enveloping algebra provides interesting examples of noncommutative and noncocommutative Hopf algebras and leads to a classification of connected Hopf algebras of Gelfand-Kirillov dimension four in [WZZ].