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Lie groups

San Martin, Luiz A. B.

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Lie groups

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lie groups/ by Luiz A. B. San Martin.
作者:	San Martin, Luiz A. B.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xiv, 371 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Lie groups. -
電子資源:	https://doi.org/10.1007/978-3-030-61824-7
ISBN:	9783030618247

Lie groups
San Martin, Luiz A. B.

Lie groups[electronic resource] /by Luiz A. B. San Martin. - Cham :Springer International Publishing :2021. - xiv, 371 p. :ill., digital ;24 cm. - Latin American mathematics series. - Latin American mathematics series..

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.

ISBN: 9783030618247

Standard No.: 10.1007/978-3-030-61824-7doiSubjects--Topical Terms:

526114
Lie groups.

LC Class. No.: QA387 / .S3613 2021

Dewey Class. No.: 512.482

Lie groups
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490 1 $a Latin American mathematics series
505 0 $a 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.
520 $a 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.
650 0 $a Lie groups. $3 526114
650 1 4 $a Topological Groups, Lie Groups. $3 891005
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Non-associative Rings and Algebras. $3 891108
650 2 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Latin American mathematics series. $3 3491620
856 4 0 $u https://doi.org/10.1007/978-3-030-61824-7
950 $a Mathematics and Statistics (SpringerNature-11649)