Macaulay2 ยป Documentation
Packages ยป LieTypes :: LieAlgebra
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LieAlgebra -- class for Lie algebras


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

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

o1 = g

o1 : simple LieAlgebra
i2 : h=simpleLieAlgebra("E",6)

o2 = h

o2 : simple LieAlgebra
i3 : g++h

o3 = ๐”ž  ++ ๐”ข
      1     6

o3 : LieAlgebra

If you have access to unicode fraktur, you can use the shorthand

i4 : ๐”ฃ_4

o4 = ๐”ฃ

o4 : simple LieAlgebra

See also new LieAlgebra from Matrix.

Functions and methods returning an object of class LieAlgebra :

Methods that use an object of class LieAlgebra :

For the programmer

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