Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group
13 Nov 2020
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Kodaka Kazunori
We consider two twisted actions of a countable discrete group on
$\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we
get two inclusions of $C^*$-algebras...We suppose that they are strongly Morita
equivalent as inclusions of $C^*$-algebras. Also, we suppose that one of the
inclusions is irreducible, that is, the relative commutant of one of the
$\sigma$-unital $C^*$-algebra in the multiplier $C^*$-algebra of the reduced
twisted crossed product is trivial. We show that the two actions are then
strongly Morita equivalent up to some automorphism of the group.(read more)