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.
Uses Mathematica (code available online) for group-theoretical constructions.
Includes a variety of physical examples from crystallography, atomic physics, cosmology and field theory.
In the years of my appointment at the Italian Embassy in Moscow among other dissemination activities I also taught for three subsequent years a course on Group Theory at MEPHI (Moscow Engineering Physics Institute) exercise for which were conducted by Prof. Alexander Fedotov. As a result of that teaching experience this Text Book was produced and published by De Gruyter in 2018.
The new book Discrete, Finite and Lie Groups has a partial overlap with Groups and Manifolds but it is different in conceptiont, pursued goals and target readers. Indeed while Group and Manifolds is a TextBook for Physics - major graduate students, the new book is conceived as an advanced reading for scholars and students of various disciplines and it aims at emphasizing the transversal role Group Theory in all branches of Mathematics including analysis. The library of Mathematica NoteBooks has been completely revised updated and systematized.
