Traces on group C*-algebras, sofic groups and L\"uck's conjecture
G\"ul Balci, Georeges Skandalis

TL;DR
This paper provides an alternative proof of L"uck's determinant conjecture for sofic groups using traces on group C*-algebras, and discusses related issues in $L^2$-Betti numbers and Atiyah's problem.
Contribution
It introduces a new proof technique for L"uck's conjecture for sofic groups based on traces on group C*-algebras, offering fresh insights.
Findings
Proof of L"uck's determinant conjecture for sofic groups
Connection between traces on group C*-algebras and L"uck's conjecture
Discussion on Atiyah's problem and $L^2$-Betti numbers
Abstract
We give an alternate proof of a Theorem of Elek and Szabo establishing L\"uck's determinant conjecture for sofic groups. Our proof is based on traces on group C*-algebras. We briefly discuss the relation with Atiyah's problem on the integrality of -Betti numbers.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Advanced Topics in Algebra
