simpleLieAlgebra -- construct a simple Lie algebra

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 $\mathfrak{a}_n$, $\mathfrak{b}_n$, $\mathfrak{c}_n$, $\mathfrak{d}_n$) corresponding to the Lie algebras $\mathfrak{sl}(n+1,\mathbb{C})$, $\mathfrak{so}(2n+1,\mathbb{C})$, $\mathfrak{sp}(2n,\mathbb{C})$, $\mathfrak{so}(2n,\mathbb{C})$ respectively, and five exceptional simple Lie algebras, $\mathfrak{e}_6$, $\mathfrak{e}_7$, $\mathfrak{e}_8$, $\mathfrak{f}_4$, $\mathfrak{g}_2$.

i1 : simpleLieAlgebra("A",1)

o1 = 𝔞
      1

o1 : simple LieAlgebra

i2 : simpleLieAlgebra("E",6)

o2 = 𝔢
      6

o2 : simple LieAlgebra

Ways to use simpleLieAlgebra:

simpleLieAlgebra(String,ZZ)

For the programmer

The object simpleLieAlgebra is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:73:0.