### 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

1.1.3 The adjoint matrices

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 *C*_{1} 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

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