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On amenability of group algebras, I

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Abstract

We study amenability of algebras and modules (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups.

We show that a group G is amenable if and only if its group ring \( \mathbb{K} \) G is amenable for some (and therefore for any) field \( \mathbb{K} \).

Similarly, a G-set X is amenable if and only if its span \( \mathbb{K} \) X is amenable as a \( \mathbb{K} \) G-module for some (and therefore for any) field \( \mathbb{K} \).

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Correspondence to Laurent Bartholdi.

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Bartholdi, L. On amenability of group algebras, I. Isr. J. Math. 168, 153–165 (2008). https://doi.org/10.1007/s11856-008-1061-7

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