By N. Bourbaki

ISBN-10: 3540434054

ISBN-13: 9783540434054

This is the English translation of Bourbaki's textual content Groupes et Algebres de Lie,

Chapters 7 to nine. It completes the formerly released translations of Chapters

1 to three (3-540-50218-1) and four to six (3-540-42650-7) by means of masking the constitution and illustration thought of

semi-simple Lie algebras and compact Lie teams.

Chapter 7 bargains with Cartan subalgebras of Lie algebras, normal components and

conjugacy theorems. bankruptcy eight starts with the constitution of cut up semi-simple Lie

algebras and their root structures. It is going directly to describe the finite-dimensional

modules for such algebras, together with the nature formulation of Hermann Weyl. It

concludes with the speculation of Chevalley orders. bankruptcy nine is dedicated to the

theory of compact Lie teams, starting with a dialogue in their maximal tori,

root platforms and Weyl teams. It is going directly to describe the illustration idea

of compact Lie teams, together with the applying of integration to set up

Weyl's formulation during this context. The bankruptcy concludes with a dialogue of the

actions of compact Lie teams on manifolds.

The 9 chapters jointly shape the main complete textual content to be had at the

theory of Lie teams and Lie algebras.