Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
MetricTensor |
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Details and Options
Examples
(2)
Basic Examples
(2)
Metric tensors of all rank 4 classical Lie algebras:
In[1]:=
MetricTensor[A4]
Out[1]=
4 5 | 3 5 | 2 5 | 1 5 |
3 5 | 6 5 | 4 5 | 2 5 |
2 5 | 4 5 | 6 5 | 3 5 |
1 5 | 2 5 | 3 5 | 4 5 |
In[2]:=
MetricTensor[B4]
Out[2]=
1 | 1 | 1 | 1 2 |
1 | 2 | 2 | 1 |
1 | 2 | 3 | 3 2 |
1 2 | 1 | 3 2 | 1 |
In[3]:=
MetricTensor[C4]
Out[3]=
1 2 | 1 2 | 1 2 | 1 2 |
1 2 | 1 | 1 | 1 |
1 2 | 1 | 3 2 | 3 2 |
1 2 | 1 | 3 2 | 2 |
In[4]:=
MetricTensor[D4]
Out[4]=
1 | 1 | 1 2 | 1 2 |
1 | 2 | 1 | 1 |
1 2 | 1 | 1 | 1 2 |
1 2 | 1 | 1 2 | 1 |
Metric tensors of all exceptional Lie algebras :
In[1]:=
MetricTensor[E6]
Out[1]=
4 3 | 5 3 | 2 | 4 3 | 2 3 | 1 |
5 3 | 10 3 | 4 | 8 3 | 4 3 | 2 |
2 | 4 | 6 | 4 | 2 | 3 |
4 3 | 8 3 | 4 | 10 3 | 5 3 | 2 |
2 3 | 4 3 | 2 | 5 3 | 4 3 | 1 |
1 | 2 | 3 | 2 | 1 | 2 |
In[2]:=
MetricTensor[E7]
Out[2]=
2 | 3 | 4 | 3 | 2 | 1 | 2 |
3 | 6 | 8 | 6 | 4 | 2 | 4 |
4 | 8 | 12 | 9 | 6 | 3 | 6 |
3 | 6 | 9 | 15 2 | 5 | 5 2 | 9 2 |
2 | 4 | 6 | 5 | 4 | 2 | 3 |
1 | 2 | 3 | 5 2 | 2 | 3 2 | 3 2 |
2 | 4 | 6 | 9 2 | 3 | 3 2 | 7 2 |
In[3]:=
MetricTensor[E8]
Out[3]=
4 | 7 | 10 | 8 | 6 | 4 | 2 | 5 |
7 | 14 | 20 | 16 | 12 | 8 | 4 | 10 |
10 | 20 | 30 | 24 | 18 | 12 | 6 | 15 |
8 | 16 | 24 | 20 | 15 | 10 | 5 | 12 |
6 | 12 | 18 | 15 | 12 | 8 | 4 | 9 |
4 | 8 | 12 | 10 | 8 | 6 | 3 | 6 |
2 | 4 | 6 | 5 | 4 | 3 | 2 | 3 |
5 | 10 | 15 | 12 | 9 | 6 | 3 | 8 |
In[4]:=
MetricTensor[F4]
Out[4]=
2 | 3 | 2 | 1 |
3 | 6 | 4 | 2 |
2 | 4 | 3 | 3 2 |
1 | 2 | 3 2 | 1 |
In[5]:=
MetricTensor[G2]
Out[5]=
2 3 | 1 |
1 | 2 |
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