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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