<p>This is the softcover reprint of the English translation of Bourbaki's text Groupes et Algèbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (978-3-540-69171-6) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.</p>

Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)

Science & Math

A. N. Pressley Nicolas Bourbaki

Mathematics

Springer, Verlag

See the best price to sell, buy, or rent books by A. N. Pressley Nicolas Bourbaki. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by A. N. Pressley Nicolas Bourbaki

See the best price to sell, buy, or rent books by A. N. Pressley Nicolas Bourbaki. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)