Problems and Solutions for Groups, Lie Groups, Lie Algebras with Applications

The following sections are included:

• Preface

• Contents

• Notation

A group G is a set of objects { a, b, c,…} (not necessarily countable)together with a binary operation which associates with any ordered pair of elements a, b in G a third element ab in G (closure). The binary operation (called group multiplication) is subject to the following requirements:

1) There exists an element e in G called the identity element (also called neutral element) such that eg = ge = g for all g ϵ G.

2) For every g ϵ G there exists an inverse element g^-1 in G such that gg^-1 = g^-1 = e

3) Associative law. The identity (ab)c = a(bc) is satisfied for all a,b,c ϵ G

Let ℝ be the field of real numbers. Let …

A Lie algebra L is a vector space over a field 𝔽 together with a bilinear map, [ , ] : L × L → L, called the Lie bracket, such that the following identities hold for all a, b, c ϵ L…

Problem 1. An icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. Let …

The following sections are included:

• Bibliography

• Index