Theory of Lie Groups

This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.

This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras.