**Identifier**

Identifier

Values

['A',1]
=>
2

['A',2]
=>
3

['B',2]
=>
4

['G',2]
=>
7

['A',3]
=>
4

['B',3]
=>
7

['C',3]
=>
6

['A',4]
=>
5

['B',4]
=>
9

['C',4]
=>
8

['D',4]
=>
8

['F',4]
=>
26

['A',5]
=>
6

['B',5]
=>
11

['C',5]
=>
10

['D',5]
=>
10

['A',6]
=>
7

['B',6]
=>
13

['C',6]
=>
12

['D',6]
=>
12

['E',6]
=>
27

['A',7]
=>
8

['B',7]
=>
15

['C',7]
=>
14

['D',7]
=>
14

['E',7]
=>
56

['A',8]
=>
9

['B',8]
=>
17

['C',8]
=>
16

['D',8]
=>
16

['E',8]
=>
248

Description

The minimal dimension of a faithful linear representation of the Lie algebra of given type.

References

[1]

**Burde, D., Moens, W.***Minimal faithful representations of reductive Lie algebras*MathSciNet:2371687Code

def statistic(C): n = C.rank() T = C.type() if T == "A": return n+1 if T == "B": if n == 2: return 4 if n >= 3: return 2*n+1 if T == "C": if n >= 3: return 2*n if T == "D": if n >= 4: return 2*n if T == "E": if n == 6: return 27 if n == 7: return 56 if n == 8: return 248 if T == "F": return 26 if T == "G": return 7

Created

Apr 19, 2018 at 19:57 by

**Martin Rubey**Updated

Apr 19, 2018 at 19:57 by

**Martin Rubey**searching the database

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