Non-Supramenable Groups Acting on Locally Compact Spaces

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product $C^*$-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed products for both amenable and non-amenable groups.

2010 Mathematics Subject Classification: 43A07, 46L55, 46L35

Keywords and Phrases: Supramenable groups, actions on locally compact spaces, purely infinite C^*-algebras and actions.

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