The $$C^*$$-algebra of the semi-direct product $$K < imes A$$
2020
Let
$$G=K < imes A$$
be the semi-direct product group of a compact group K acting on an abelian locally compact group A. We describe the
$$C^*$$
-algebra
$$C^*(G)$$
of G in terms of an algebra of operator fields defined over the spectrum of G, generalizing previous results obtained for some special classes of such groups.
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