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
Symmetry Groups and Their Applicationsby Willard Miller - Academic Press
A beginning graduate level book on applied group theory. Only those aspects of group theory are treated which are useful in the physical sciences, but the mathematical apparatus underlying the applications is presented with a high degree of rigor.
(18093 views)
Congruence Lattices of Finite Algebrasby William DeMeo - arXiv
We review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist...
(11162 views)
An Introduction to Group Theory: Applications to Mathematical Music Theoryby Flor Aceff-Sanchez, et al. - BookBoon
In this text, a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, is introduced.
(12858 views)
Group Theory: Birdtracks, Lie's, and Exceptional Groupsby Predrag Cvitanovic - Princeton University Press
A book on the theory of Lie groups for researchers and graduate students in theoretical physics and mathematics. It answers what Lie groups preserve trilinear, quadrilinear, and higher order invariants. Written in a lively and personable style.
(18003 views)