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Springer Undergraduate Mathematics Ser.: Matrix Groups : An Introduction to Lie Group Theory by Andrew Baker (2001, Trade Paperback)

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Matrix Groups: An Introduction to Lie Group Theory

About this product

Product Identifiers

PublisherSpringer London, The Limited

ISBN-101852334703

ISBN-139781852334703

eBay Product ID (ePID)1955536

Product Key Features

Number of PagesXi, 330 Pages

Publication NameMatrix Groups : an Introduction to Lie Group Theory

LanguageEnglish

SubjectGroup Theory, Algebra / Linear, Matrices, Topology

Publication Year2001

TypeTextbook

Subject AreaMathematics

AuthorAndrew Baker

SeriesSpringer Undergraduate Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Weight21.7 Oz

Item Length9.3 in

Item Width7 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2001-049261

Dewey Edition21

ReviewsFrom the reviews of the first edition:MATHEMATICAL REVIEWS"This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited backgroundâ€¦The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate studentsâ€¦To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory.""This book is an introduction to Lie group theory with focus on the matrix case. â€¦ This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003), From the reviews of the first edition: MATHEMATICAL REVIEWS "This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited backgroundâ€¦The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate studentsâ€¦To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." "This book is an introduction to Lie group theory with focus on the matrix case. â€¦ This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003), From the reviews of the first edition: MATHEMATICAL REVIEWS "This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background...The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students...To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." "This book is an introduction to Lie group theory with focus on the matrix case. ... This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003), From the reviews of the first edition: MATHEMATICAL REVIEWS "This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited backgrounda? The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate studentsa? To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." "This book is an introduction to Lie group theory with focus on the matrix case. a? This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal512/.2

Table Of ContentI. Basic Ideas and Examples.- 1. Real and Complex Matrix Groups.- 2. Exponentials, Differential Equations and One-parameter Subgroups.- 3. Tangent Spaces and Lie Algebras.- 4. Algebras, Quaternions and Quaternionic Symplectic Groups.- 5. Clifford Algebras and Spinor Groups.- 6. Lorentz Groups.- II. Matrix Groups as Lie Groups.- 7. Lie Groups.- 8. Homogeneous Spaces.- 9. Connectivity of Matrix Groups.- III. Compact Connected Lie Groups and their Classification.- 10. Maximal Tori in Compact Connected Lie Groups.- 11. Semi-simple Factorisation.- 12. Roots Systems, Weyl Groups and Dynkin Diagrams.- Hints and Solutions to Selected Exercises.

SynopsisAimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter. The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions. Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry., This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

LC Classification NumberQA252.3