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DETECTING IDEALS IN REDUCED CROSSED PRODUCT C*-ALGEBRAS OF TOPOLOGICAL DYNAMICAL SYSTEMS
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 16 December 2025, pp. 1-25
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We introduce the
$\ell ^1$-ideal intersection property for crossed product 
${\mathrm {C}}^*$-algebras. It is implied by 
${\mathrm {C}}^*$-simplicity as well as 
${\mathrm {C}}^*$-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the 
$\ell ^1$-ideal intersection property. On the way, we extend previous results on 
${\mathrm {C}}^*$-uniqueness of 
-groupoid algebras to the general twisted setting.
-groupoid algebras to the general twisted setting.