Amenability of coarse spaces and K-algebras Articles uri icon

publication date

  • August 2018

start page

  • 257

end page

  • 306

issue

  • 2

volume

  • 8

International Standard Serial Number (ISSN)

  • 1664-3607

Electronic International Standard Serial Number (EISSN)

  • 1664-3615

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.

keywords

  • amenability; paradoxical decompositions; følner nets; coarse spaces; unital k -algebras; leavitt path algebras; translation algebras