Properties
The module structure of a representation of a Hopf algebra H is simply its structure as a module for the underlying associative algebra. The main use of considering the additional structure of a Hopf algebra is when considering all H-modules as a category. The additional structure is also used to define invariant elements of an H-module V. An element v in V is invariant under H if for all h in H, where ε is the counit of H. The subset of all invariant elements of V forms a submodule of V.
Read more about this topic: Representation Theory Of Hopf Algebras
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