Representation Theory of Hopf Algebras - Representations On An Algebra

Representations On An Algebra

A Hopf algebra also has representations which carry additional structure, namely they are algebras.

Let H be a Hopf algebra. If A is an algebra with the product operation, and is a representation of H on A, then ρ is said to be a representation of H on an algebra if μ is H-equivariant. As special cases, Lie algebras, Lie superalgebras and groups can also have representations on an algebra.