Groups and manifolds: lectures for physicists with examples in mathematica/ Pietro Giuseppe Fre and Alexander Fedotov

Includes bibliography

Fundamental notations of algebra -- Groups: a bestiary for beginners -- Basic elements of finite group theory -- Finite subgroups of SA(3) crystallographic groups -- Manifolds and lie groups -- Structure of lie algebras -- Root systems and their classification -- Lie algebra representation theory -- Exceptional lie algebras -- A primary on the theory of connections and metrics -- Isometries and the geometry of coset manifolds -- An anthology of group theory physical applications -- Exercises -- Mathematica Notebooks

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.