### The Lie Algebras su(N), an Introduction

• Preface
• 1 Lie algebras
• 1.1 Definition
• 1.1.1 What is a Lie algebra
1.1.2 The structure constants
1.1.4 The Killing form
1.1.5 Simplicity
1.1.6 Example
• 1.2 Isomorphism of Lie algebras
• 1.3 Operators and functions
• 1.3.1 The general set-up
1.3.2 Further properties
• 1.4 Representation of a Lie algebra
• 1.5 Reducible and irreducible representations, multiplets.
• 2 The Lie algebras su(N)
• 2.1 Hermitian matrices
2.2 Definition
2.3 Structure constants of su(N)
• 3 The Lie algebra su(2)
• 3.1 The generators of the su(2)-algebra.
3.2 Operators constituting the algebra su(2)
3.3 Multiplets of su(2)
3.4 Irreducible representations of the su(2)-algebra
3.5 Direct products of irreducible representations and their function sets.
3.6 Reduction of direct products of su(2)-representations and multiplets.
3.7 Graphical reduction of direct products of su(2)-multiplets.
• 4 The Lie algebra su(3)
• 4.1 The generators of the su(3)-algebra.
4.2 Subalgebras of the su(3)-algebra.
4.3 Step operators and states in su(3)
4.4 Multiplets of su(3)
4.5 Individual states of the su(3)-multiplet and their multiplicities.
4.6 Dimension of the su(3)-multiplet.
4.7 The smallest su(3)-multiplets.
4.8 The fundamental multiplet of su(3).
4.9 The hypercharge Y.
4.10 Irreducible representations of the su(3) algebra.
4.11 Casimir operators.
4.12 The eigenvalue of the Casimir operator C1 in su(3).
4.13 Direct products of su(3)-multiplets.
4.14 Decomposition of direct products of multiplets by means of Young diagrams.
• 5 The Lie algebra su(4)
• 5.1 The generators of the su(4)-algebra, subalgebras.
5.2 Step operators and states in su(4).
5.3 Multiplets of su(4).
5.4 The charm C.
5.5 Direct products of su(4)-multiplets.
5.6 The Cartan–Weyl basis of su(4).
• 6 General properties of the su(N)-algebras
• 6.1 Elements of the su(N)-algebra.
6.2 Multiplets of su(N). References Index
• References
• Index