Amenability of coarse spaces and K-algebras. Ara, P., Li, K., Lledó, F., & Wu, J. *Bulletin of Mathematical Sciences*, 8(2):257–306, August, 2018. tex.ids= AraLiLledoWu2018Amenabilityb arXiv: 1607.00328Paper doi abstract bibtex 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 commutative 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.

@article{ara_amenability_2018-1,
title = {Amenability of coarse spaces and {K}-algebras},
volume = {8},
issn = {1664-3607, 1664-3615},
url = {https://arxiv.org/abs/1607.00328},
doi = {10.1007/s13373-017-0109-6},
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 commutative 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.},
language = {en},
number = {2},
urldate = {2021-06-03},
journal = {Bulletin of Mathematical Sciences},
author = {Ara, Pere and Li, Kang and Lledó, Fernando and Wu, Jianchao},
month = aug,
year = {2018},
note = {tex.ids= AraLiLledoWu2018Amenabilityb
arXiv: 1607.00328},
keywords = {16P90, 43A07, 37A15, 20F65, 16S99, Mathematics - Metric Geometry, Mathematics - Operator Algebras, Mathematics - Rings and Algebras},
pages = {257--306},
}

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