Lie Groups

Beschreibung

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications.
Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.
This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications.
Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.
Presents Lie theory from its fundamental principles, as a special class of groups that are studied using differential and integral calculus methods Offers several exercises at the end of each chapter, to check and reinforce comprehension Each chapter of the book begins with a general, straightforward introduction to the concepts covered, before the formal definitions are presented

Autor*in

Luiz A. B. San Martin

Themen in »Lie Groups«

Lie groups Lie algebras Topological group Haar measure Homomorphism Enveloping algebras Compact groups Nilpotent Lie group action

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“An important feature of the book is the presence of a lot of examples illustrating introduced concepts and proven results. Each chapter … accompanied by a fairly many exercises that enable the reader to check the degree of understanding of the material in each chapter and to learn something new. The student can use this book for self-study of the foundations of the theory of Lie groups.” (V. V. Gorbatsevich, zbMATH 1466.22001, 2021)
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