Amenability of coarse spaces and -algebras
In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for local ly finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with pro...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:228076 |
| Acceso en línea: | https://ddd.uab.cat/record/228076 https://dx.doi.org/urn:doi:10.1007/s13373-017-0109-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Amenability Paradoxical decompositions Følner nets Coarse spaces Unital -algebras Leavitt path algebras Translation algebras 16P90 43A07 37A15 20F65 16S99 |
| Sumario: | In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for local ly finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenability of the corresponding translation algebra. |
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