Compact Lie Groups

Mark R. Sepanski

ISBN 10: 1441921389 / ISBN 13: 9781441921383

Published by Springer New York, 2010

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Provides an approach that minimizes advanced prerequisitesSelf-contained and systematic exposition requiring no previous exposure to Lie theoryAdvances quickly to the Peter-Weyl Theorem and its corresponding Fourier theoryStreamlined.

Seller Inventory # 4172670

Bibliographic Details

• Title: Compact Lie Groups
• Publisher: Springer New York
• Publication Date: 2010
• Language: English
• ISBN 10: 1441921389
• ISBN 13: 9781441921383
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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. Coverage includes 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 book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.

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.

From the Back Cover

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.