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 Seminar series.

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