Congruence subgroups and the Atiyah conjecture

Details Congruence subgroups and the Atiyah conjecture Congruence subgroups and the Atiyah conjecture

2005-11-30

arxiv.org/abs/math/0511747v2

Mathematics

Rings and Algebras

Second version: 14 pages. Minor corrections and changes, some due to helpful comments by the referee

Scientific paper

Let A denote the algebraic closure of the rationals Q in the complex numbers C. Suppose G is a torsion-free group which contains a congruence subgroup as a normal subgroup of finite index and denote by U(G) the C-algebra of closed densely defined unbounded operators affiliated to the group von Neumann algebra. We prove that there exists a division ring D(G) such that A[G] < D(G) < U(G). This establishes some versions of the Atiyah conjecture for the group G.

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