Minimal dynamical systems on prime C*-algebras
| Autor: | Kirchberg, Eberhard, Phillips, N. Christopher |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give a number of examples of exotic actions of locally compact groups on separable nuclear C*-algebras. In particular, we give examples of the following: (1) Minimal effective actions of ${\mathbb{Z}}$ and $F_n$ on unital nonsimple prime AF algebras. (2) For any second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra. (3) For any amenable second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra (unital when the group is ${\mathbb{Z}}$ or ${\mathbb{R}}$) such that the crossed product is $K \otimes {\mathcal{O}}_2$ (${\mathcal{O}}_2$ when the group is ${\mathbb{Z}}$). (4) For any second countable locally compact abelian group which is not discrete, an action on $K \otimes {\mathcal{O}}_2$ such that the crossed product is a nonsimple prime C*-algebra. In most of these situations, we can specify the primitive ideal space of the C*-algebra (of the crossed product in the last item) within a class of spaces. Comment: This paper was nearly done about 10 years ago, but was pushed aside under the press of other projects, and then forgotten. It is now being posted, after Kirchberg's death. The key preprint of Harnisch and Kirchberg was never published and has disappeared from the website of the Universitaet Muenster. It is temporarily at: https://pages.uoregon.edu/ncp/Research/Misc/heft399.pdf |
| Databáze: | arXiv |
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