Algebra Seminar

Algebraic topologists have studied connected compact Lie groups for the past sixty years. One early success was to establish a clear connection between the homology of a Lie group and its Weyl group. This study also made clear that the classifying space of a Lie group could be used to formulate a great deal of information about the group and its homology. It has been a long standing question as to just what information could be so formulated.

These considerations have lead to the creation, for each prime p, of a theory of p-compact groups. Basically one is studying connected compact Lie groups via their classifying spaces but in a more general setting, relying on a few key properties. The pattern obtained both incorporates and generalizes the classification of semi-simple Lie groups. Rather than being based on Weyl groups the pattern is based on p-adic reflection groups.

I will try to explain the above remarks keeping clear of technical issues.