Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
Algebra |
Details and Options
Examples
(1)
Basic Examples
(1)
Classical Lie algebras can be entered in three different ways, which all evaluate to their unique internal representation: by the traditional name, by their Dynkin classification or by the internal representation:
In[1]:=
{SU5,A4,Algebra[A][4]}//InputForm
Out[1]//InputForm=
{Algebra[A][4], Algebra[A][4], Algebra[A][4]}
In[2]:=
B4//TraditionalForm
Out[2]//TraditionalForm=
SO(9)
In[3]:=
SO10//StandardForm
Out[3]//StandardForm=
D
5
The input and internal representation of exceptional algebras is the same and the display forms are nearly the same:
In[4]:=
{InputForm[#],StandardForm[#],TraditionalForm[#]}&@{E6,E7,E8,F4,G2}
Out[4]=
{{E6,E7,E8,F4,G2},{,,,,},{,,,,}}
E
6
E
7
E
8
F
4
G
2
E
6
E
7
E
8
F
4
G
2
Determining the algebra of irreps, weights or roots:
In[5]:=
Algebra[Irrep[A][0,1,0,0]]
Out[5]=
SU(5)
In[6]:=
Algebra[Weight[A][0,2,0,-1]]
Out[6]=
SU(5)
In[7]:=
Algebra[RootOmega[B][2,-1,0,0]]
Out[7]=
SO(9)
 |
|
""