國立高雄大學圖資館 |

Language: English

Back

Lie groups

San Martin, Luiz A. B.

Lie groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lie groupsby Luiz A. B. San Martin.
Author:	San Martin, Luiz A. B.
Published:	Cham :Springer International Publishing :2021.
Description:	xiv, 371 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Lie groups.
Online resource:	https://doi.org/10.1007/978-3-030-61824-7
ISBN:	9783030618247$q(electronic bk.)

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$q(electronic bk.)

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

190898
Lie groups.

LC Class. No.: QA387 / .S3613 2021

Dewey Class. No.: 512.482

Lie groups
LDR:02581nmm a2200349 a 4500 001 600642
003 DE-He213
005 20210616145244.0
006 m d
007 cr nn 008maaau
008 211104s2021 sz s 0 eng d
020 $a 9783030618247$q(electronic bk.)
020 $a 9783030618230$q(paper)
024 7 $a 10.1007/978-3-030-61824-7 $2 doi
035 $a 978-3-030-61824-7
040 $a GP $c GP
041 1 $a eng $h por
050 4 $a QA387 $b .S3613 2021
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.482 $2 23
090 $a QA387 $b .S227 2021
100 1 $a San Martin, Luiz A. B. $3 895275
240 1 0 $a Grupos de Lie. $l English
245 1 0 $a Lie groups $h [electronic resource] / $c by Luiz A. B. San Martin.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xiv, 371 p. : $b ill., digital ; $c 24 cm.
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 190898
650 1 4 $a Topological Groups, Lie Groups. $3 273787
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Non-associative Rings and Algebras. $3 274087
650 2 4 $a Algebraic Geometry. $3 274807
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Latin American mathematics series. $3 895276
856 4 0 $u https://doi.org/10.1007/978-3-030-61824-7
950 $a Mathematics and Statistics (SpringerNature-11649)