Compact Lie Groups [electronic resource] / edited by Mark R. Sepanski.
Contributor(s): Sepanski, Mark R [editor.] | SpringerLink (Online service)Material type: TextSeries: Graduate Texts in Mathematics: 235Publisher: New York, NY : Springer New York, 2007Description: XIII, 201 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387491585Subject(s): Mathematics | Associative rings | Rings (Algebra) | Matrix theory | Algebra | Topological groups | Lie groups | Mathematical analysis | Analysis (Mathematics) | Differential geometry | Mathematics | Topological Groups, Lie Groups | Linear and Multilinear Algebras, Matrix Theory | Associative Rings and Algebras | Differential Geometry | AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 512.55 | 512.482 LOC classification: QA252.3QA387Online resources: Click here to access online
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Compact Lie Groups -- Representations -- HarmoniC Analysis -- Lie Algebras -- Abelian Lie Subgroups and Structure -- Roots and Associated Structures -- Highest Weight Theory.
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups. Key Features: • Provides an approach that minimizes advanced prerequisites • Self-contained and systematic exposition requiring no previous exposure to Lie theory • Advances quickly to the Peter–Weyl Theorem and its corresponding Fourier theory • Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations • Exercises sprinkled throughout This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful.