Matrix Groups

An Introduction to Lie Group Theory

Andrew Baker

330 pages, parution le 21/01/2002

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Résumé

Aimed 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.

Contents:

Part I. Basic Ideas and Examples: Real and Complex Matrix Groups.

Exponentials, Differential Equations and One Parameter Subgroups.
Tangent Spaces and Lie Algebras. Algebras, Quaternions, and Symplectic Groups.
Clifford Algebras and Spinor Groups. Lorentz Groups.

Part II. Matrix Groups as Lie Groups: Lie groups.

Homogeneous Spaces.
Connectivity of Matrix Groups.

Part III. Compact Connected Lie Groups and their Classification: Maximal Tori in Compact

Connected Lie Groups.
Semi-simple Factorization.
Roots systems, Weyl Groups and Dynkin Diagrams.

Bibliography.
Index.

L'auteur - Andrew Baker

Andrew Baker is Lecturer at the School of Politics and International Studies at the Queen's University of Belfast. He is the-co-editor of Governing Financial Globalisation (Routledge, 2005) and has published in journals such as Review of International Political Economy and Global Governance.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Andrew Baker
Parution	21/01/2002
Nb. de pages	330
Format	17 x 23,5
Couverture	Broché
Poids	567g
Intérieur	Noir et Blanc
EAN13	9781852334703
ISBN13	978-1-85233-470-3