Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
CartanMatrix |
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Details and Options
Examples
(1)
Basic Examples
(1)
Cartan matrix of all rank 4 classical Lie algebras:
In[1]:=
CartanMatrix[A4]
Out[1]=
2 | -1 | 0 | 0 |
-1 | 2 | -1 | 0 |
0 | -1 | 2 | -1 |
0 | 0 | -1 | 2 |
In[2]:=
CartanMatrix[B4]
Out[2]=
2 | -1 | 0 | 0 |
-1 | 2 | -1 | 0 |
0 | -1 | 2 | -2 |
0 | 0 | -1 | 2 |
In[3]:=
CartanMatrix[C4]
Out[3]=
2 | -1 | 0 | 0 |
-1 | 2 | -1 | 0 |
0 | -1 | 2 | -1 |
0 | 0 | -2 | 2 |
In[4]:=
CartanMatrix[D4]
Out[4]=
2 | -1 | 0 | 0 |
-1 | 2 | -1 | -1 |
0 | -1 | 2 | 0 |
0 | -1 | 0 | 2 |
Cartan matrix of all exceptional Lie algebras:
In[5]:=
CartanMatrix[E6]
Out[5]=
2 | -1 | 0 | 0 | 0 | 0 |
-1 | 2 | -1 | 0 | 0 | 0 |
0 | -1 | 2 | -1 | 0 | -1 |
0 | 0 | -1 | 2 | -1 | 0 |
0 | 0 | 0 | -1 | 2 | 0 |
0 | 0 | -1 | 0 | 0 | 2 |
In[6]:=
CartanMatrix[E7]
Out[6]=
2 | -1 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -1 | 0 | 0 | 0 | 0 |
0 | -1 | 2 | -1 | 0 | 0 | -1 |
0 | 0 | -1 | 2 | -1 | 0 | 0 |
0 | 0 | 0 | -1 | 2 | -1 | 0 |
0 | 0 | 0 | 0 | -1 | 2 | 0 |
0 | 0 | -1 | 0 | 0 | 0 | 2 |
In[7]:=
CartanMatrix[E8]
Out[7]=
2 | -1 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -1 | 0 | 0 | 0 | 0 | 0 |
0 | -1 | 2 | -1 | 0 | 0 | 0 | -1 |
0 | 0 | -1 | 2 | -1 | 0 | 0 | 0 |
0 | 0 | 0 | -1 | 2 | -1 | 0 | 0 |
0 | 0 | 0 | 0 | -1 | 2 | -1 | 0 |
0 | 0 | 0 | 0 | 0 | -1 | 2 | 0 |
0 | 0 | -1 | 0 | 0 | 0 | 0 | 2 |
In[8]:=
CartanMatrix[F4]
Out[8]=
2 | -1 | 0 | 0 |
-1 | 2 | -2 | 0 |
0 | -1 | 2 | -1 |
0 | 0 | -1 | 2 |
In[9]:=
CartanMatrix[G2]
Out[9]=
2 | -1 |
-3 | 2 |
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