Toda lattice, cohomology of compact Lie groups and finite Chevalley groups

Innnite Dimensional Lie Groups and the Two-dimensional Toda Lattice

The Waring Problem for Lie Groups and Chevalley Groups

The classical Waring problem deals with expressing every natural number as a sum of g(k) k powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given word w 6= 1. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed word w 6= 1 and for a classical ...

Cohomology of Lie groups and Lie algebras

The aim of this expository essay is to illustrate one example of a local-to-global phenomenon. What we mean by that is better illustrated by explaining the topic at hand. We aim to understand the de Rham cohomology groups of a Lie group. But instead of doing it using actual differential forms, we shall use the properties of a Lie group (especially the fact that it is a group) to reduce calculat...

Lie Groups and p-Compact Groups

A p-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of p-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on homotopy theoretic considerations. 1 From compact Lie groups to p-co...

The cohomology of Lie groups

Let G be a simple Lie group with a maximal torus T . We construct the cohomology ring H∗(G; Z) in terms of Schubert classes on G/T . 2000 Mathematical Subject Classification: 55T10; 14M15