Sofic representations of amenable groups

By Gábor Elek, Endre Szabó. 2010

75 citations recorded by the source corpus.

Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileably amenable subgroup is sofic as well. We show that the restriction is unnecessary; the free product of two sofic groups amalgamated over an arbitrary amenable subgroup is sofic. We also prove a group theoretical analogue of a result of Kenley Jung. A finitely generated group is amenable if and only if it has only one sofic representation up to conjugacy equivalence.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5fa6dbb4fa6276da251a2690cba82cbe904ebe09

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In Geometry and Topology

1. Ben Hayes
2. Valerio Capraro
3. Martino Lupini
4. Lewis Bowen
5. David Kerr
6. Hanfeng Li
7. William Slofstra

In Mathematical Physics

1. Ben Hayes
2. Valerio Capraro
3. Martino Lupini
4. Lewis Bowen
5. David Kerr
6. Hanfeng Li
7. William Slofstra

Citations in the corpus

• Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The fact that free product of sofic groups amalgamated over an amenable groups is sofic has been shown in [29] in the particular case of amenable monotileable groups and in [40] and [95] in full generality.”
• Sofic entropy and amenable groups (2010, methodology): “This motivates the next result, which is a minor extension of [ES10], Theorem 2.”
• Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “The class of sofic groups contains all amenable groups, all residually finite groups, all linear groups and is closed under direct unions and free products with amalgamation over amenable subgroups (see [16],[14],[36],[38]).”