Discrete, Finite and Lie Groups

Pietro G. Fré, born in Alessandria in 1952, is Professor Emeritus of Theoretical Physics at the University of Turin. He was Dean of the Department of Physics until his retirement on November 1st 2022. He was Director of the Arnold-Regge Center for Algebra, Geometry and Theoretical Physics from 2017 to 2022. From 1996 to 2000 he was President of SIGRAV (Italian Society of General Relativity and Physics of Gravitation). He was Professor of Theoretical Physics and Director of the Particle Physics Sector at SISSA from 1990 to 1996. Fellow of the Theoretical Division of CERN, post-doctoral fellow at the California Institute of Technology and the University of Bielefeld in the early years of his career. Author of about 380 scientific publications including 9 monographic books, he has given relevant contributions to the field of Supergravity and String Theories with applications to Cosmology, Black Holes, Holographic Gauge/Gravity Correspondence and to the development of the underlying Mathematical Structures. We mention in particular the introduction of the rheonomic formulation (with R. D'Auria), the invention, independently from mathematicians, under the name of "Cartan Integrable Systems" of Free Differential Algebras and their extension with fermionic p-forms, the D'Auria-Fré algebra which later evolved into the so named A-infinity algebras, the geometric formulation of the theory in 11-dimensions (M-theory), the geometric systematization of the Lagrangian of N = 2 Supergravity (with S. Ferrara et al), the discovery of some of the seven dimensional homogeneous Sasakian varieties and the early development of their holographic equivalents via quivers. Since 2001, Prof. Frè has started an intense collaboration with Ukraine and Russia. In 2002 he spent a sabbatical year in Kiev and taught a long course in Supergravity at the Bogoliubov Institute of the Ukrainian Academy of Sciences. A frequent visitor to the Joint Institute of Nuclear Research in Dubna, in the years from

"This beautiful book offers a thorough and cohesive presentation of group theory and related concepts, which lie at the core of modern natural sciences and engineering, and whose relevance nowadays extends even to social sciences. As the author argues, the topic of group theory should be an essential part of scientific education, and should be taught aiming to a high degree of abstraction: this is reflected in the structure of this book, which starts from simple notions and progressively moves towards deeper, more abstract and mathematically more powerful concepts. The text is characterized by the unique style of its author: a style that is mathematically very rigorous but at the same time also highly enjoyable, with occasional historical references and enlightening examples. A must read." Prof. Marco Panero, University of Turin, Department of Physics