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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 257-306 |
| Number of pages | 50 |
| Journal | Bulletin of Mathematical Sciences |
| Volume | 8 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 1 2018 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
}
Amenability of coarse spaces and K -algebras. / Ara, Pere; Li, Kang; Lledó, Fernando; Wu, Jianchao.
In: Bulletin of Mathematical Sciences, Vol. 8, No. 2, 01.08.2018, p. 257-306.Research output: Contribution to journal › Article
TY - JOUR
T1 - Amenability of coarse spaces and K -algebras
AU - Ara, Pere
AU - Li, Kang
AU - Lledó, Fernando
AU - Wu, Jianchao
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85049786709&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049786709&partnerID=8YFLogxK
U2 - 10.1007/s13373-017-0109-6
DO - 10.1007/s13373-017-0109-6
M3 - Article
VL - 8
SP - 257
EP - 306
JO - Bulletin of Mathematical Sciences
JF - Bulletin of Mathematical Sciences
SN - 1664-3607
IS - 2
ER -