Identifier
Identifier
Values
['A',1] generating graphics... => 2
['A',2] generating graphics... => 3
['B',2] generating graphics... => 4
['G',2] generating graphics... => 7
['A',3] generating graphics... => 4
['B',3] generating graphics... => 7
['C',3] generating graphics... => 6
['A',4] generating graphics... => 5
['B',4] generating graphics... => 9
['C',4] generating graphics... => 8
['D',4] generating graphics... => 8
['F',4] generating graphics... => 26
['A',5] generating graphics... => 6
['B',5] generating graphics... => 11
['C',5] generating graphics... => 10
['D',5] generating graphics... => 10
['A',6] generating graphics... => 7
['B',6] generating graphics... => 13
['C',6] generating graphics... => 12
['D',6] generating graphics... => 12
['E',6] generating graphics... => 27
['A',7] generating graphics... => 8
['B',7] generating graphics... => 15
['C',7] generating graphics... => 14
['D',7] generating graphics... => 14
['E',7] generating graphics... => 56
['A',8] generating graphics... => 9
['B',8] generating graphics... => 17
['C',8] generating graphics... => 16
['D',8] generating graphics... => 16
['E',8] generating graphics... => 248
click to show generating function       
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:2371687
Code
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