Umfang:
Online-Ressource (XVI, 196p. 44 illus, digital)
Ausgabe:
First
ISBN:
9780387788661
,
9781280390937
,
0387788662
,
128039093X
Serie:
Universitext
Inhalt:
General Facts About Groups -- Representations of Finite Groups -- Representations of Compact Groups -- Lie Groups and Lie Algebras -- Lie Groups SU(2) and SO(3) -- Representations of SU(2) and SO(3) -- Spherical Harmonics -- Representations of SU(3) and Quarks.
Inhalt:
Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: • Brisk review of the basic definitions of group theory, with examples • Representation theory of finite groups: character theory • Representations of compact groups using the Haar measure • Lie algebras and linear Lie groups • Detailed study of SO(3) and SU(2), and their representations • Spherical harmonics • Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraits and a few historical remarks. With only linear algebra and calculus as prerequisites, Groups and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom and for independent study.
Anmerkung:
Includes bibliographical references and index
,
""Contents""; ""Introduction""; ""Acknowledgments""; ""1 General Facts About Groups""; ""1 Review of Definitions""; ""2 Examples of Finite Groups""; ""2.1 Cyclic Group of Order n""; ""2.2 Symmetric Group Sn""; ""2.3 Dihedral Group""; ""2.4 Other Examples""; ""3 Examples of Infinite Groups""; ""4 Group Actions and Conjugacy Classes""; ""References""; ""Exercises""; ""2 Representations of Finite Groups""; ""1 Representations""; ""1.1 General Facts""; ""1.2 Irreducible Representations""; ""1.3 Direct Sum of Representations""; ""1.4 Intertwining Operators and Schur's Lemma""
,
""2 Characters and Orthogonality Relations""""2.1 Functions on a Group, Matrix Coefficients""; ""2.2 Characters of Representations and Orthogonality Relations""; ""2.3 Character Table""; ""2.4 Application to the Decomposition of Representations""; ""3 The Regular Representation""; ""3.1 Definition""; ""3.2 Character of the Regular Representation""; ""3.3 Isotypic Decomposition""; ""3.4 Basis of the Vector Space of Class Functions""; ""4 Projection Operators""; ""5 Induced Representations""; ""5.1 Definition""; ""5.2 Geometric Interpretation""; ""References""; ""Exercises""
,
""3 Representations of Compact Groups""""1 Compact Groups""; ""2 Haar Measure""; ""3 Representations of Topological Groups and Schur's Lemma""; ""3.1 General Facts""; ""3.2 Coefficients of a Representation""; ""3.3 Intertwining Operators""; ""3.4 Operations on Representations""; ""3.5 Schur's Lemma""; ""4 Representations of Compact Groups""; ""4.1 Complete Reducibility""; ""4.2 Orthogonality Relations""; ""5 Summary of Chapter 3""; ""References""; ""Exercises""; ""4 Lie Groups and Lie Algebras""; ""1 Lie Algebras""; ""1.1 Definition and Examples""; ""1.2 Morphisms""
,
""1.3 Commutation Relations and Structure Constants""""1.4 Real Forms""; ""1.5 Representations of Lie Algebras""; ""2 Review of the Exponential Map""; ""3 One-Parameter Subgroups of GL(n,K)""; ""4 Lie Groups""; ""5 The Lie Algebra of a Lie Group""; ""6 The Connected Component of the Identity""; ""7 Morphisms of Lie Groups and of Lie Algebras""; ""7.1 Differential of a Lie Group Morphism""; ""7.2 Differential of a Lie Group Representation""; ""7.3 The Adjoint Representation""; ""References""; ""Exercises""; ""5 Lie Groups SU(2) and SO(3)""; ""1 The Lie Algebras su(2) and so(3) ""
,
""1.1 Bases of su(2)""""1.2 Bases of so(3)""; ""1.3 Bases of sl(2,C)""; ""2 The Covering Morphism of SU(2) onto SO(3)""; ""2.1 The Lie Group SO(3)""; ""2.2 The Lie Group SU(2)""; ""2.3 Projection of SU(2) onto SO(3)""; ""References""; ""Exercises""; ""6 Representations of SU(2) and SO(3)""; ""1 Irreducible Representations of sl(2, C)""; ""1.1 The Representations Dj""; ""1.2 The Casimir Operator""; ""1.3 Hermitian Nature of the Operators J3 and J2""; ""2 Representations of SU(2)""; ""2.1 The Representations Dj""; ""2.2 Characters of the Representations Dj""; ""3 Representations of SO(3)""
,
""References""
Weitere Ausg.:
ISBN 9780387788654
Weitere Ausg.:
Buchausg. u.d.T. Kosmann-Schwarzbach, Yvette, 1941 - Groups and symmetries New York, NY : Springer, 2010 ISBN 0387788654
Weitere Ausg.:
ISBN 9780387788654
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Endliche Gruppe
;
Lie-Gruppe
;
Darstellungstheorie
;
Gruppentheorie
DOI:
10.1007/978-0-387-78866-1
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
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