@article{a64dc16dfb774752bf738bf3e56e796a,
title = "Amenability of coarse spaces and K -algebras",
abstract = "In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally 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.",
author = "Pere Ara and Kang Li and Fernando Lled{\'o} and Jianchao Wu",
note = "Funding Information: Acknowledgements The second-named author is partially supported by Deutsche Forschungsgemein-schaft (SFB 878). The third-named author thanks Wilhelm Winter for his kind invitation to the Mathematics Department of the University of M{\"u}nster in April 2014 and March–June 2016. Financial support was provided by the DFG through SFB 878, as well as, by a DAAD-Grant during these visits. He would also like to thank the organizers of the Thematic Program on Abstract Harmonic Analysis, Banach and Operator Algebras at Fields Institute in Toronto in May 2014 for the stimulating atmosphere. The fourth-named author are grateful to David Kerr for some very helpful suggestions. We are also grateful to Javier Rodr{\'i}guez Chatruc for his comments on Section 6. Part of the researc h was conducted during visits and workshops at Universi-tat Aut{\`o}noma de Barcelona, University of Copenhagen, University of M{\"u}nster and Institut Mittag–Leffler. The authors owe many thanks and great appreciation to these institutes and hosts for their hospitality. Funding Information: P. Ara Supported by the Grants DGI MICIIN MTM2011-28992-C02-01 and MINECO MTM2014-53644-P. K. Li Supported by ERC Advanced Grant No. OAFPG 247321, the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Danish Council for Independent Research (DFF-5051-00037). F. Lled{\'o} Supported by Projects DGI MTM2012-36732-C03-01, MTM2014-54692-P and Severo Ochoa SEV-2015-0554 of the Spanish Ministry of Economy and Competition (MINECO), Spain. J. Wu Supported by SFB 878 Groups, Geometry and Actions and ERC Advanced Grant ToDyRiC 267079. Funding Information: The second-named author is partially supported by Deutsche Forschungsgemeinschaft (SFB 878). The third-named author thanks Wilhelm Winter for his kind invitation to the Mathematics Department of the University of M{\"u}nster in April 2014 and March–June 2016. Financial support was provided by the DFG through SFB 878, as well as, by a DAAD-Grant during these visits. He would also like to thank the organizers of the Thematic Program on Abstract Harmonic Analysis, Banach and Operator Algebras at Fields Institute in Toronto in May 2014 for the stimulating atmosphere. The fourth-named author are grateful to David Kerr for some very helpful suggestions. We are also grateful to Javier Rodr{\'i}guez Chatruc for his comments on Section 6. Part of the researc h was conducted during visits and workshops at Universitat Aut{\`o}noma de Barcelona, University of Copenhagen, University of M{\"u}nster and Institut Mittag–Leffler. The authors owe many thanks and great appreciation to these institutes and hosts for their hospitality. P. Ara Supported by the Grants DGI MICIIN MTM2011-28992-C02-01 and MINECO MTM2014-53644-P. K. Li Supported by ERC Advanced Grant No. OAFPG 247321, the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Danish Council for Independent Research (DFF-5051-00037). F. Lled{\'o} Supported by Projects DGI MTM2012-36732-C03-01, MTM2014-54692-P and Severo Ochoa SEV-2015-0554 of the Spanish Ministry of Economy and Competition (MINECO), Spain. J. Wu Supported by SFB 878 Groups, Geometry and Actions and ERC Advanced Grant ToDyRiC 267079. Publisher Copyright: {\textcopyright} 2017, The Author(s).",
year = "2018",
month = aug,
day = "1",
doi = "10.1007/s13373-017-0109-6",
language = "English (US)",
volume = "8",
pages = "257--306",
journal = "Bulletin of Mathematical Sciences",
issn = "1664-3607",
publisher = "Springer Basel AG",
number = "2",
}