# simpleLieAlgebra -- construct a simple Lie algebra

## Synopsis

• Usage:
simpleLieAlgebra("A",1)
• Inputs:
• t, , the type of the root system of the desired Lie algebra
• k, an integer, the rank of the desired Lie algebra
• Outputs:
• g, an instance of the type LieAlgebra, the simple Lie algebra with the given rank and type

## Description

The classification of simple Lie algebras over the complex numbers is well known. There are four infinite families (types A, B, C, D) corresponding to the Lie algebras $sl(n+1,\mathbb{C})$, $so(2n+1,\mathbb{C})$, $sp(2n,\mathbb{C})$, $so(2n,\mathbb{C})$ respectively, and five exceptional simple Lie algebras, E6, E7, E8, F4, G2.

 i1 : simpleLieAlgebra("A",1) o1 = Simple Lie algebra, type A, rank 1 o1 : LieAlgebra i2 : simpleLieAlgebra("E",6) o2 = Simple Lie algebra, type E, rank 6 o2 : LieAlgebra

## Ways to use simpleLieAlgebra :

• "simpleLieAlgebra(String,ZZ)"

## For the programmer

The object simpleLieAlgebra is .