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＜電子ブック＞
Lie Groups / by Luiz A. B. San Martin
(Latin American Mathematics Series. ISSN:25246763)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XIV, 371 p. 25 illus : online resource
著者標目	*San Martin, Luiz A. B author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Group theory LCSH:Nonassociative rings LCSH:Algebraic geometry FREE:Topological Groups and Lie Groups FREE:Group Theory and Generalizations FREE:Non-associative Rings and Algebras FREE:Algebraic Geometry
一般注記	Preface -- Introduction -- Part I: Topological Groups -- Topological Groups -- Haar Measure -- Representations of Compact Groups -- Part II: Lie Groups and Algebras -- Lie Groups and Lie Algebras -- Lie Subgroups -- Homomorphism and Coverings -- Series Expansions -- Part III: Lie Algebras and Simply Connected Groups -- The Affine Group and Semi-direct Products -- Solvable and Nilpotent Groups -- Compact Groups -- Noncompact Semi-simple Groups -- Part IV: Transformation Groups -- Lie Group Actions -- Invariant Geometry -- Appendices 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 HTTP:URL=https://doi.org/10.1007/978-3-030-61824-7

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