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# 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.