Group Hopf Algebra - Symmetries of Group Actions

Symmetries of Group Actions

Let G be a group and X a topological space. Any action of G on X gives a homomorphism, where F(X) is an appropriate algebra of k-valued functions, such as the Gelfand-Naimark algebra of continuous functions vanishing at infinity. is defined by with the adjoint defined by

for, and .

This may be described by a linear mapping

where, are the elements of G, and, which has the property that group-like elements in kG give rise to automorphisms of F(X).

endows F(X) with an important extra structure, described below.

Read more about this topic:  Group Hopf Algebra

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