Congruence subgroups and the Atiyah conjecture
环与代数
2007-05-23 v2 泛函分析
几何拓扑
摘要
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.
引用
@article{arxiv.math/0511747,
title = {Congruence subgroups and the Atiyah conjecture},
author = {Daniel R. Farkas and Peter A. Linnell},
journal= {arXiv preprint arXiv:math/0511747},
year = {2007}
}
备注
Second version: 14 pages. Minor corrections and changes, some due to helpful comments by the referee