On the Topology of Kac-Moody groups

Details On the Topology of Kac-Moody groups On the Topology of Kac-Moody groups

2008-10-05

arxiv.org/abs/0810.0851v1

Mathematics

Algebraic Topology

Scientific paper

We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T with normalizer N(T). In this article we study the (co)homology of K as a Hopf algebra. In particular, if F has positive characteristic, we show that the homology H(K,F) is a finitely generated algebra, and that the cohomology is finitely generated only if K is a compact Lie group . We also study the stable homotopy type of the classifying space BK and show that it is a retract of the classifying space BN(T) of N(T). We illustrate our results with the example of rank two Kac-Moody groups.

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