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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