Lectures on Lie groups / W.Y. Hsiang.

Format:

Book

Author/Creator:

Hsiang, Wu Yi, 1937-

Series:

Series on university mathematics

Series on university mathematics ; v. 2

Language:

English

Subjects (All):

Lie groups.

Physical Description:

1 online resource (115 p.)

Place of Publication:

River Edge, N.J. : World Scientific, c2000.

Language Note:

English

Summary:

This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints.

Contents:

Lecture 1 Linear Groups and Linear Representations; 1. Basic Concepts and Definitions; 2. A Brief Overview; 3. Compact Groups, Haar Integral and the Averaging Method; 4. Frobenius-Schur Orthogonality and the Character Theory; 5. Classification of Irreducible Complex Representations of S3; 6. L2(G) and Concluding Remarks; Lecture 2 Lie Groups and Lie Algebras; 1. One-parameter Subgroups and Lie Algebras; 2. Lie Subgroups and the Fundamental Theorem of Lie; 3. Lie Homomorphisms and Simply Connected Lie Groups; 4. Adjoint Actions and Adjoint Representations

Lecture 3 Orbital Geometry of the Adjoint Action1. Bi-invariant Riemannian Structure on a Compact Connected Lie Group and the Maximal Tori Theorem of É Cartan; 2. Root System and Weight System; 3. Classification of Rank 1 Compact Connected Lie Groups; Lecture 4 Coxeter Groups, Weyl Reduction and Weyl Formulas; 1. Geometry of Coxeter Groups; 2. Geometry of (W,h) and the Root System; 3. The Volume Function and Weyl Integral Formula; 4. Weyl Character Formula and Classification of Complex Irreducible Representations; Lecture 5 Structural Theory of Compact Lie Algebras

1. Characterization of Compact Lie Algebras2. Cartan Decomposition and Structural Constants of Compact Lie Algebras; Lecture 6 Classification Theory of Compact Lie Algebras and Compact Connected Lie Groups; 1. Classification of Simple Compact Lie Algebras; 2. Classification of Geometric Root Patterns; 3. Classical Compact Lie Groups and Their Root Systems

Notes:

Description based upon print version of record.

ISBN:

1-281-86962-7

9786611869625

981-238-478-2

OCLC:

475900375