Sofic groups and direct finiteness
By G. Elek, Endre Szabó. 2003
107 citations recorded by the source corpus.
Abstract We construct an analogue of von Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic groups.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/53367c3c979ff94f9a1041cfaed03e03d8c660d8
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- David J. Aldous
- Valerio Capraro
- Martino Lupini
- Á. Backhausz
- Tullio Ceccherini-Silberstein
- Michel Coornaert
- Balázs Szegedy
- Russell Lyons
In Mathematical Physics
- Russell Lyons
- Valerio Capraro
- Martino Lupini
- Tullio Ceccherini-Silberstein
- David J. Aldous
- Michel Coornaert
- Balázs Szegedy
- Andreas Thom
Citations in the corpus
- Action convergence of operators and graphs (2018, background): “A positive answer to this question would imply that every group is sofic and it would solve several important open problems in group theory (see, e.g., [15]).”
- Injective linear cellular automata and sofic groups (2007, methodology): “As an immediate consequence of Theorem 1.2 and 1.3, we deduce the following result, which has been previously established by G. Elek and A. Szab´o [ ES1 ] using different methods (their proof involves embeddings of the group rings into continuous von Neumann regular rings).”
- Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The rest of this section is dedicated to the proof from [37] that sofic groups satisfy Kaplansky’s direct finiteness conjecture.”
- Processes on Unimodular Random Networks (2006, background): “Some references for the latter work, showing relations to von Neumann algebras and logic, among other things, are Feldman and Moore (1977a, 1977b), Feldman, Hahn, and Moore (1978), Connes, Feldman, and Weiss (1981), Zimmer (1984), Kechris and Miller (2004), Becker and Kechris (1996), Kechris (1991),”
- FINITARY APPROXIMATIONS OF GROUPS AND THEIR APPLICATIONS (2017, methodology): “Major applications of this notion arose in the work of Elek and Szabó [2004] on Kaplansky’s Direct Finiteness Conjecture, on Lück’s Determinant Conjecture by Elek and Szabó [2005], and more recently in joint work of Klyachko and Thom [2017] on generalizations of the Kervaire-Laudenbach Conjecture an”