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Published online by Cambridge University Press: 20 November 2018
An invariant is presented which classifies, up to equivariant isomorphism, ${{C}^{*}}$-dynamical systems arising as limits from inductive systems of elementary
${{C}^{*}}$-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.