**Introduction to Lie Groups, Adjoint Action and Some Generalizations**

by Marcos M. Alexandrino, Renato G. Bettiol

**Publisher**: arXiv 2010**Number of pages**: 129

**Description**:

The main purpose of these lecture notes is to provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming mostly at advanced undergraduate and graduate students. A special focus is given to maximal tori and roots of compact Lie groups, exploring its connection with isoparametric submanifolds and polar actions.

Download or read it online for free here:

**Download link**

(1MB, PDF)

## Similar books

**Lectures on Lie Groups and Representations of Locally Compact Groups**

by

**F. Bruhat**-

**Tata Institute of Fundamental Research**

We consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. We have rigidly adhered to the analytic approach in establishing the relations between Lie groups and Lie algebras.

(

**11396**views)

**Roots of a Compact Lie Group**

by

**Kristopher Tapp**-

**arXiv**

This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary abstractions.

(

**7971**views)

**Group Theory: Birdtracks, Lie's, and Exceptional Groups**

by

**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.

(

**16361**views)

**Algebraic Groups, Lie Groups, and their Arithmetic Subgroups**

by

**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.

(

**13013**views)