TY - JOUR
AU - Kodaka, Kazunori
PY - 2021/08/31
Y2 - 2022/01/23
TI - Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 127
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-125997
UR - https://www.mscand.dk/article/view/125997
SP - 317-336
AB - <p>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 of $C^*$-algebras 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.</p>
ER -