Ultraproducts and the Atiyah conjecture

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• Peter Linnell (Virginia Tech)
• Wednesday 28 October 2009, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Jan Saxl.

Let G be a group. Then there is a von Neumann regular algebra U(G) containing the complex group algebra CG. One version of the Atiyah conjecture states that if G is torsion-free, then there is a division ring D such that CG < D < U(G). Let K denote the algebraic closure of the rationals in C. In many cases, it can be proven that there is a division ring D such that KG < D < U(G). In this talk, results on the Atiyah conjecture will be presented, in particular when G is a pro-p group, and then how one can go from KG to CG. This will involve the use of ultraproducts, which will be described.

This talk is part of the Algebra and Representation Theory Seminar series.

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