LieAlgebra -- class for Lie algebras

Description

This class represents Lie algebras. Currently only simple Lie algebras over the complex numbers are supported. An object of type LieAlgebra is a hash table whose keys record whether the Lie algebra is simple, the rank of the Lie algebra, and the type of the root system.

i1 : g=simpleLieAlgebra("A",1)

o1 = g

o1 : LieAlgebra

i2 : g=simpleLieAlgebra("E",6)

o2 = g

o2 : LieAlgebra

Functions and methods returning an object of class LieAlgebra :

simpleLieAlgebra -- construct a simple Lie algebra

Methods that use an object of class LieAlgebra :

"dualCoxeterNumber(LieAlgebra)" -- see dualCoxeterNumber -- returns the dual Coxeter number of a simple Lie algebra
expression(LieAlgebra) (missing documentation)
"highestRoot(LieAlgebra)" -- see highestRoot -- returns the highest root of a simple Lie algebra
"irreducibleLieAlgebraModule(List,LieAlgebra)" -- see irreducibleLieAlgebraModule -- construct the irreducible Lie algebra module with given highest weight
"KillingForm(LieAlgebra,List,List)" -- see KillingForm -- computes the scaled Killing form applied to two weights
LieAlgebra == LieAlgebra -- tests equality of LieAlgebra
net(LieAlgebra) (missing documentation)
"positiveRoots(LieAlgebra)" -- see positiveRoots -- returns the positive roots of a simple Lie algebra
"starInvolution(List,LieAlgebra)" -- see starInvolution -- computes w* for a weight w
"weylAlcove(ZZ,LieAlgebra)" -- see weylAlcove -- the dominant integral weights of level less than or equal to l

For the programmer

The object LieAlgebra is a type, with ancestor classes HashTable < Thing.