LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.55
Dewey Class	512.482
Title	Matrix Groups ([EBook] :) : An Introduction to Lie Group Theory / / by Andrew Baker.
Author	Baker, Andrew
Other name(s)	SpringerLink (Online service)
Publication	London : : Springer London : : Imprint: Springer, , 2002.
Physical Details	XI, 330 p. : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9781447101833
Summary Note	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 note	I. 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4471-0183-3
Links to Related Works	Subject References: Algebra . Differential Geometry . Group theory . Group Theory and Generalizations . Lie groups . Linear and Multilinear Algebras, Matrix Theory . Mathematics . Matrix theory . Physics . Theoretical, Mathematical and Computational Physics . Topological groups . Topological groups, Lie groups . Authors: Baker, Andrew . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 512.482 . 512.55 .

Catalogue Display

Matrix Groups: An Introduction to Lie Group Theory /

Reviews