Algebra 4: Lie Algebras, Chevalley Groups, and Their Representations

This book covers Lie algebra and representation theory, including semisimple Lie algebras, root systems, and Chevalley groups, with motivating illustrations and exercises for understanding and solving problems.

Format: Paperback / softback
Length: 321 pages
Publication date: 31 March 2022
Publisher: Springer Verlag, Singapore

This comprehensive fourth book in a four-volume series on algebra delves into the intricate realms of Lie algebra and representation theory, providing a detailed exploration of these subjects. It encompasses a wide range of topics, including semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups, and representation theory of Chevalley groups. To enhance the understanding of readers, numerous motivating illustrations are accompanied by comprehensive exercises, enabling them to grasp the concepts and apply them to find precise or realistic solutions to their problems.

The book begins by introducing the fundamental concepts of Lie algebras, including their structure, properties, and applications. It then delves into the study of root systems, which play a crucial role in understanding the structure and representation theory of Lie algebras. The representation theory of Lie algebra is explored in depth, covering topics such as linear transformations, Jordan normal forms, and the representation theory of compact Lie groups.

Chevalley groups are introduced as a powerful tool for studying Lie algebras and their representations. The book discusses the construction of Chevalley groups, their properties, and their applications to various problems in mathematics. Representation theory of Chevalley groups is also explored, including the representation theory of finite groups, semisimple Lie algebras, and their applications to quantum mechanics.

Throughout the book, numerous examples and exercises are provided to illustrate the theoretical concepts and help readers apply them to real-world problems. These exercises range from simple to challenging, allowing readers to build their skills and confidence in solving complex algebraic equations and problems.

In conclusion, this book is an essential resource for students and researchers interested in Lie algebra and representation theory. It provides a comprehensive and up-to-date introduction to these subjects, covering both the theoretical foundations and practical applications. With its clear explanations, numerous illustrations, and extensive exercises, it enables readers to develop a deep understanding of these topics and apply them to their research and professional endeavors.

Weight: 516g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811604775
Edition number: 1st ed. 2021