Luiz A. B. San Martin: Lie Groups | Buch

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Cover: 9783030618230 | Lie Groups | Luiz A. B. San Martin | Buch | HC runder Rücken kaschiert

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Sprache: Englisch

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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.

Über den Autor

Luiz Antonio Barrera San Martin is a Full Professor at the University of Campinas, Brazil. He holds a Master's degree in Mathematics (1982) from the University of Campinas, Brazil, and a PhD in Mathematics (1987) from the University of Warwick, England. His research interests are in Lie Theory, more precisely in semigroups, semisimple groups, Lie groups, homogeneous spaces, and flag manifolds.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	388
Reihe:	Latin American Mathematics Series
Inhalt:	xiv 371 S. 25 s/w Illustr. 371 p. 25 illus.
ISBN-13:	9783030618230
ISBN-10:	3030618234
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	San Martin, Luiz A. B.
Auflage:	1st ed. 2021
Hersteller:	Springer International Publishing Latin American Mathematics Series
Maße:	241 x 160 x 27 mm
Von/Mit:	Luiz A. B. San Martin
Erscheinungsdatum:	24.02.2021
Gewicht:	0,746 kg

preigu-id: 118954503