simpleLieAlgebra -- construct a simple Lie algebra

Synopsis

Usage:

simpleLieAlgebra("A",1)
Inputs:
- t, a string, 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 a method function.

simpleLieAlgebra -- construct a simple Lie algebra

Synopsis

Description

Ways to use simpleLieAlgebra :

For the programmer

Ways to use `simpleLieAlgebra` :