Lie Groups and Lie Algebras

The book is dedicated to exploring the recent advancements in Lie theory and its practical applications in addressing complex equations and models motivated by physical and biological phenomena. It encompasses a range of topics including the analysis and classification of Lie algebras which stand as the invariance algebras of models reflecting real-world scenarios. A significant portion of the content delves into the Lie and conditional symmetry classification problems of nonlinear partial differential equations (PDEs) highlighting the utility of symmetry-based methods in deriving new exact solutions to nonlinear PDEs relevant to various applications.Furthermore this book includes articles and reviews that shed light on the theoretical underpinnings of symmetry-based methods showcasing their efficacy in solving a wide array of linear and nonlinear models. Through this comprehensive coverage the book aims to equip readers with a deep understanding of Lie theory's foundational principles and its instrumental role in advancing the solution of complex equations and models across different scientific disciplines.