Cohomology of Lie groups made discrete

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...

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

The Cohomology of Lie Groups

We follow the computations in [2], [5], and [8] to deduce the cohomology rings of various Lie groups (SU(n), U(n), Sp(n) with Z-coefficients and SO(n), Spin(n), G2, F4, E6, E7, E8 with field coefficients) using the Serre spectral sequence.

Cyclic Cohomology for Discrete Groups

We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups