# Math 674: Lie Groups and Algebras

## Contents

## Catalog Information

### Title

Lie Groups and Algebras

### Credit Hours

3

### Offered

Upon request.

### Prerequisite

673, equivalent, or teacher approval.

### Description

Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory. Other topics may be presented.

## Desired Learning Outcomes

### Prerequisites

Math 673 or equivalent.

### Minimal learning outcomes

Students will master the basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory. Possible applications to physics or to other areas of mathematics.

### Textbooks

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

### Additional topics

Any advanced topic in Algebra including Galois theory, Grobner bases, Representation theory, Invariant theory, etc.

### Courses for which this course is prerequisite

None.