1 results
The maximal injective crossed product
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 11 / November 2020
- Published online by Cambridge University Press:
- 22 April 2019, pp. 2995-3014
- Print publication:
- November 2020
-
- Article
-
- You have access
- Open access
- Export citation
-
A crossed product functor is said to be injective if it takes injective morphisms to injective morphisms. In this paper we show that every locally compact group
$G$ admits a maximal injective crossed product 
$A\mapsto A\rtimes _{\text{inj}}G$. Moreover, we give an explicit construction of this functor that depends only on the maximal crossed product and the existence of 
$G$-injective 
$C^{\ast }$-algebras; this is a sort of ‘dual’ result to the construction of the minimal exact crossed product functor, the latter having been studied for its relationship to the Baum–Connes conjecture. It turns out that 
$\rtimes _{\text{inj}}$ has interesting connections to exactness, the local lifting property, amenable traces, and the weak expectation property.
