國立虎尾科技大學 |

Lie Groups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lie Groups/ by Luiz A. B. San Martin.
Author:	San Martin, Luiz A. B.
Description:	XIV, 371 p. 25 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Topological groups. -
Online resource:	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. - 1st ed. 2021. - XIV, 371 p. 25 illus.online resource. - Latin American Mathematics Series,2524-6763. - 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:

885827
Topological groups.

LC Class. No.: QA252.3

Dewey Class. No.: 512.55

Lie Groups
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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.
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650 0 $a Lie groups. $3 527929
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650 0 $a Nonassociative rings. $3 1254916
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