Group Hopf Algebra - Hopf Algebra Structure

Hopf Algebra Structure

We give kG the structure of a cocommutative Hopf algebra by defining the coproduct, counit, and antipode to be the linear extensions of the following maps defined on G:

The required Hopf algebra compatibility axioms are easily checked. Notice that, the set of group-like elements of kG (i.e. elements such that and ), is precisely G.

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