Download or read book Groups and Manifolds written by Pietro Giuseppe Fré and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.