Algebra and Topology Seminar

4pm Tuesday 10 December 2002

Roozbeh Hazrat
MSI

Valuation Theory for division algebras, Application to reduced K-theory

A division ring is a very elementary object. It is just a vector space with an associative product structure where each non-zero element has an inverse. A central simple algebra is just a set of matrices over a division algebra. A classical theorem of Wedderburn shows that simple algebras are basic building blocks of ring theory. Despite the simplicity of the definition, the study of these objects has come to involve a large collection of mathematical tools and view points.

In this talk, we apply the valuation theory for division algebras which has been developed during the last 20 years to study the Whitehead group K₁ and descending central series of a division algebra. In particular we determine the descending central series for some classes of division algebras.




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