Introduction to Complex Semisimple Lie Algebras

Author: Meng Daoji
Publisher:
Publish Date: 1999-06-01
Features: The theory of Lie groups and Lie algebras has undergone tremendous development since its inception and has a close connection with disciplines such as theoretical physics. It has now become an indispensable branch of mathematics, known as Lie theory. Complex semisimple Lie algebras are the foundational, most important, most complete, and most perfect part of Lie theory. This book comprehensively and systematically discusses the fundamental theory of complex semisimple Lie algebras. The book is divided into seven chapters. The content includes: the basic concepts of Lie algebras, criteria for determining the semisimplicity, nilpotency, and solvability of Lie algebras, the structure, existence, classification, finite-dimensional representations, and exceptional Lie algebras of complex semisimple Lie algebras, and more. The book presents the content in an accessible and progressive manner, making it suitable for teaching. It includes numerous examples to illustrate abstract theories and provides a moderate number of exercises to develop students' skills. The book is tightly centered around complex semisimple Lie algebras, showcasing their perfect theory and captivating content to readers. Additionally, it connects to the theme by introducing its relationships with various branches such as real semisimple Lie algebras, algebraic groups, modular Lie algebras, Kac-Moody algebras, and complete Lie algebras, as well as the research achievements that permeate these fields. This lays a solid foundation for readers to further study Lie theory and makes it easier for them to enter the forefront of research. This book can serve as a textbook for senior undergraduate and graduate students in mathematics departments of comprehensive universities, as well as for graduate students and researchers in theoretical physics and related fields.