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＜電子ブック＞
Matrix Groups : An Introduction to Lie Group Theory / by Andrew Baker
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2002.
出版者	London : Springer London : Imprint: Springer
出版年	2002
本文言語	英語
大きさ	XI, 330 p : online resource
著者標目	*Baker, Andrew author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Algebras, Linear LCSH:Geometry, Differential LCSH:Mathematical physics LCSH:Group theory FREE:Topological Groups and Lie Groups FREE:Linear Algebra FREE:Differential Geometry FREE:Theoretical, Mathematical and Computational Physics FREE:Group Theory and Generalizations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-0183-3

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