Amenability of coarse spaces and K-algebras

作者：Ara Pere^*; Li Kang; Lledo Fernando; Wu Jianchao

来源：Bulletin of Mathematical Sciences, 2018, 8(2): 257-306.

DOI：10.1007/s13373-017-0109-6

• Amenability
• Paradoxical decompositions
• Folner nets
• Coarse spaces
• Unital K-algebras
• Leavitt path algebras
• Translation algebras

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.

• 出版日期2018-8