**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

**Thin Groups and Superstrong Approximation**

by

**Emmanuel Breuillard, Hee Oh (eds.)**-

**Cambridge University Press**

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.

(

**3854**views)

**Elements of Group Theory**

by

**F. J. Yndurain**-

**arXiv**

The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.

(

**13242**views)

**Groups and Semigroups: Connections and Contrasts**

by

**John Meakin**-

**University of Nebraska-Lincoln**

In the present paper, I will discuss some of these connections between group theory and semigroup theory, and I will also discuss some rather surprising contrasts between the theories. I will focus primarily on the theory of inverse semigroups.

(

**6615**views)

**Lie groups and Lie algebras**

by

**N. Reshetikhin, V. Serganova, R. Borcherds**-

**UC Berkeley**

From the table of contents: Tangent Lie algebras to Lie groups; Simply Connected Lie Groups; Hopf Algebras; PBW Theorem and Deformations; Lie algebra cohomology; Engel's Theorem and Lie's Theorem; Cartan Criterion, Whitehead and Weyl Theorems; etc.

(

**9292**views)