Lie Groups - Luiz A. B. San Martin

Lie Groups

Buch | Hardcover
XIV, 371 Seiten
2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-61823-0 (ISBN)
85,59 inkl. MwSt
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.

lt;b>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.

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.

"An important feature of the book is the presence of a lot of examples illustrating introduced concepts and proven results. Each chapter ... accompanied by a fairly many exercises that enable the reader to check the degree of understanding of the material in each chapter and to learn something new. The student can use this book for self-study of the foundations of the theory of Lie groups." (V. V. Gorbatsevich, zbMATH 1466.22001, 2021)

“An important feature of the book is the presence of a lot of examples illustrating introduced concepts and proven results. Each chapter … accompanied by a fairly many exercises that enable the reader to check the degree of understanding of the material in each chapter and to learn something new. The student can use this book for self-study of the foundations of the theory of Lie groups.” (V. V. Gorbatsevich, zbMATH 1466.22001, 2021)

Erscheinungsdatum
Reihe/Serie Latin American Mathematics Series
Zusatzinfo XIV, 371 p. 25 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 746 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte compact groups • Enveloping algebras • Haar measure • Homomorphism • Lie Algebras • Lie group action • Lie groups • Nilpotent • topological group
ISBN-10 3-030-61823-4 / 3030618234
ISBN-13 978-3-030-61823-0 / 9783030618230
Zustand Neuware
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