Cohomology of Lie groups

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.

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups

On the Cohomology of Finite Groups of Lie Type

Let IFq denote the finite field with q elements and let G = XIFq be a connected (not necessarily split) reductive group scheme over spec(IFq) . We will be interested in the cohomology of the finite groups G(IFqn) of IFqn–rational points of G , with coefficients in ZZ/` where ` is a prime different from p = char(IFq) . These groups are closely related and present special cases of the groups refe...