An Elementary Introduction to Groups and Representations
by Brian C. Hall
Publisher: arXiv 2000
Number of pages: 128
Description:
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.
Download or read it online for free here:
Download link
(950KB, PDF)
Similar books
Notes on Categories and Groupoidsby P. J. Higgins - Van Nostrand Reinhold
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(11345 views)
Theory and Applications of Finite Groupsby G. A. Miller, H. F. Blichfeldt, L. E. Dickson - J. Wiley
The book presents in a unified manner the more fundamental aspects of finite groups and their applications, and at the same time preserves the advantage which arises when each branch of an extensive subject is written by a specialist in that branch.
(5051 views)
Theory of Groups of Finite Orderby William Burnside - Cambridge University Press
After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; etc.
(6923 views)
Algebraic Groups, Lie Groups, and their Arithmetic Subgroupsby J. S. Milne
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
(8920 views)