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...

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Detalles Bibliográficos
Autores: Ara, Pere|||0000-0003-3739-9599, Li, Kang, Lledó, Fernando|||0000-0003-0861-9695, Wu, Jianchao
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
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oai_identifier_str oai:ddd.uab.cat:228076
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spelling Amenability of coarse spaces and -algebrasAra, Pere|||0000-0003-3739-9599Li, KangLledó, Fernando|||0000-0003-0861-9695Wu, JianchaoAmenabilityParadoxical decompositionsFølner netsCoarse spacesUnital -algebrasLeavitt path algebrasTranslation algebras16P9043A0737A1520F6516S99In 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. 22018-01-0120182018-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/228076https://dx.doi.org/urn:doi:10.1007/s13373-017-0109-6reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-28992-C02-01Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-53644Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2012-36732-C03-01Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-54692-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 SEV-2015-0554European Commission https://doi.org/10.13039/501100000780 267079open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2280762026-06-06T12:50:31Z
dc.title.none.fl_str_mv Amenability of coarse spaces and -algebras
title Amenability of coarse spaces and -algebras
spellingShingle Amenability of coarse spaces and -algebras
Ara, Pere|||0000-0003-3739-9599
Amenability
Paradoxical decompositions
Følner nets
Coarse spaces
Unital -algebras
Leavitt path algebras
Translation algebras
16P90
43A07
37A15
20F65
16S99
title_short Amenability of coarse spaces and -algebras
title_full Amenability of coarse spaces and -algebras
title_fullStr Amenability of coarse spaces and -algebras
title_full_unstemmed Amenability of coarse spaces and -algebras
title_sort Amenability of coarse spaces and -algebras
dc.creator.none.fl_str_mv Ara, Pere|||0000-0003-3739-9599
Li, Kang
Lledó, Fernando|||0000-0003-0861-9695
Wu, Jianchao
author Ara, Pere|||0000-0003-3739-9599
author_facet Ara, Pere|||0000-0003-3739-9599
Li, Kang
Lledó, Fernando|||0000-0003-0861-9695
Wu, Jianchao
author_role author
author2 Li, Kang
Lledó, Fernando|||0000-0003-0861-9695
Wu, Jianchao
author2_role author
author
author
dc.subject.none.fl_str_mv Amenability
Paradoxical decompositions
Følner nets
Coarse spaces
Unital -algebras
Leavitt path algebras
Translation algebras
16P90
43A07
37A15
20F65
16S99
topic Amenability
Paradoxical decompositions
Følner nets
Coarse spaces
Unital -algebras
Leavitt path algebras
Translation algebras
16P90
43A07
37A15
20F65
16S99
description 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.
publishDate 2018
dc.date.none.fl_str_mv 2
2018-01-01
2018
2018-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/228076
https://dx.doi.org/urn:doi:10.1007/s13373-017-0109-6
url https://ddd.uab.cat/record/228076
https://dx.doi.org/urn:doi:10.1007/s13373-017-0109-6
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-28992-C02-01
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-53644
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2012-36732-C03-01
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-54692-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 SEV-2015-0554
European Commission https://doi.org/10.13039/501100000780 267079
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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