Theory of groups and symmetries : finite groups, Lie groups, and Lie algebras /
Alexey P. Isaev, N.N. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, M.V. Lomonosov Moscow State University, Valery A. Rubakov, Institute for Nuclear Research, Russian Academy of Sciences, Moscow, M.V. Lomonosov Moscow State University.
- xv, 458 pages : illustrations ; 24 cm
Includes bibliographical references and index.
"The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles -- the Standard Model -- is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics"--
9789813236851 981323685X
2018001918
Group theory. Group algebras. Finite groups. Lie groups. Lie algebras.