An Elementary Introduction to Groups and Representations
by Brian C. Hall
Publisher: arXiv 2000
Number of pages: 128
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the exponential mapping, the basics of representations theory, the Baker-Campbell-Hausdorff formula, a detailed study of the representations of SU(3), and a brief survey of the representation theory of general semisimple groups.
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This book focuses on recent developments concerning various quantitative aspects of thin groups. It provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory, and combinatorics.
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