generic derivation : delta:=
mat((xi(1,1),xi(1,2),0,0,0,0),(xi(2,1),xi(2,2),0,0,0,0),(xi(3,1),xi(3,2),xi(2,2)
 + xi(1,1),0,0,0),(xi(4,1),xi(4,2),xi(3,2),xi(2,2) + 2*xi(1,1),xi(1,2),xi(4,6)),
(xi(5,1),xi(5,2), - xi(3,1),xi(2,1),2*xi(2,2) + xi(1,1),xi(5,6)),(xi(6,1),xi(6,2
),0,0,0,xi(6,6)))$
$


        [0  0  0  0  0  0]
        [                ]
        [0  0  0  0  0  0]
        [                ]
        [0  1  0  0  0  0]
adx1 := [                ]
        [0  0  1  0  0  0]
        [                ]
        [0  0  0  0  0  0]
        [                ]
        [0  0  0  0  0  0]



        [0   0  0  0  0  0]
        [                 ]
        [0   0  0  0  0  0]
        [                 ]
        [-1  0  0  0  0  0]
adx2 := [                 ]
        [0   0  0  0  0  0]
        [                 ]
        [0   0  1  0  0  0]
        [                 ]
        [0   0  0  0  0  0]



        [0   0   0  0  0  0]
        [                  ]
        [0   0   0  0  0  0]
        [                  ]
        [0   0   0  0  0  0]
adx3 := [                  ]
        [-1  0   0  0  0  0]
        [                  ]
        [0   -1  0  0  0  0]
        [                  ]
        [0   0   0  0  0  0]


The generic nilpotent derivation : the eigenvalues are 0

xi(6,6):=0

And the matrix A:=(xi(1,1),xi(1,2)),(xi(2,1),xi(2,2)) is nilpotent

We hence get 2 cases acoording to whether A neq 0 or A=0.

We consider here the case 2 where A = 0.

In that case, one may suppose A:=((0,0),(0,0)).

xi(1,1):=0,xi(1,2):=0,xi(2,1):=0,xi(2,2):=0

by subtracting adjoints one then may suppose:

xi(3,1):=0,xi(3,2):=0,xi(4,1):=0

delta:=

[   0        0     0  0  0     0   ]
[                                  ]
[   0        0     0  0  0     0   ]
[                                  ]
[   0        0     0  0  0     0   ]
[                                  ]
[   0     xi(4,2)  0  0  0  xi(4,6)]
[                                  ]
[xi(5,1)  xi(5,2)  0  0  0  xi(5,6)]
[                                  ]
[xi(6,1)  xi(6,2)  0  0  0     0   ]


We denote this delta by the shortform

shortformdelta:={xi(4,2),

                 xi(4,6),

                 ss,

                 xi(5,1),

                 xi(5,2),

                 xi(5,6),

                 ss,

                 xi(6,1),

                 xi(6,2)}

paramindexeslist:={{4,2},{4,6},{5,1},{5,2},{5,6},{6,1},{6,2}}

a:=1$

delta:=
mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,1),(1,0,0,0,0,0),(0,0,0
,0,0,0))$
$

shortformdelta:={0,1,ss,1,0,0,ss,0,0}$

on resout l'equation {{0,1},0} qui est  maintenant AA:= - d(0,5)$

Unknown: d(0,5)
Unknown: d(0,5)
bonne inconnue W:=d(0,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,1},1} qui est  maintenant AA:= - d(1,5)$

Unknown: d(1,5)
Unknown: d(1,5)
bonne inconnue W:=d(1,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,1},2} qui est  maintenant AA:= - d(2,5)$

Unknown: d(2,5)
Unknown: d(2,5)
bonne inconnue W:=d(2,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,1},3} qui est  maintenant AA:= - (d(3,5) + d(2,0))$

Unknowns: {d(3,5),d(2,0)}
Unknowns: {d(3,5),d(2,0)}
bonne inconnue W:=d(3,5)$

sa valeur doit etre WW:= - d(2,0)$

on resout l'equation {{0,1},4} qui est  maintenant AA:=d(6,1) - d(4,5) - d(3,0)$

Unknowns: {d(6,1),d(4,5),d(3,0)}
Unknowns: {d(6,1),d(4,5),d(3,0)}
bonne inconnue W:=d(6,1)$

sa valeur doit etre WW:=d(4,5) + d(3,0)$

on resout l'equation {{0,1},5} qui est  maintenant AA:= - d(5,5) + d(1,1) + d(0,
0)$

Unknowns: {d(5,5),d(1,1),d(0,0)}
Unknowns: {d(5,5),d(1,1),d(0,0)}
bonne inconnue W:=d(5,5)$

sa valeur doit etre WW:=d(1,1) + d(0,0)$

on resout l'equation {{0,1},6} qui est  maintenant AA:= - d(6,5)$

Unknown: d(6,5)
Unknown: d(6,5)
bonne inconnue W:=d(6,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,2},3} qui est  maintenant AA:=d(1,0)$

Unknown: d(1,0)
Unknown: d(1,0)
bonne inconnue W:=d(1,0)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,2},4} qui est  maintenant AA:=d(6,2)$

Unknown: d(6,2)
Unknown: d(6,2)
bonne inconnue W:=d(6,2)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,2},5} qui est  maintenant AA:= - d(3,0) + d(1,2)$

Unknowns: {d(3,0),d(1,2)}
Unknowns: {d(3,0),d(1,2)}
bonne inconnue W:=d(3,0)$

sa valeur doit etre WW:=d(1,2)$

on resout l'equation {{0,3},4} qui est  maintenant AA:=d(6,3)$

Unknown: d(6,3)
Unknown: d(6,3)
bonne inconnue W:=d(6,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,3},5} qui est  maintenant AA:=d(2,0) + d(1,3)$

Unknowns: {d(2,0),d(1,3)}
Unknowns: {d(2,0),d(1,3)}
bonne inconnue W:=d(2,0)$

sa valeur doit etre WW:= - d(1,3)$

on resout l'equation {{0,4},4} qui est  maintenant AA:=d(6,4)$

Unknown: d(6,4)
Unknown: d(6,4)
bonne inconnue W:=d(6,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,4},5} qui est  maintenant AA:=d(1,4)$

Unknown: d(1,4)
Unknown: d(1,4)
bonne inconnue W:=d(1,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,6},0} qui est  maintenant AA:= - d(0,4)$

Unknown: d(0,4)
Unknown: d(0,4)
bonne inconnue W:=d(0,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,6},2} qui est  maintenant AA:= - d(2,4)$

Unknown: d(2,4)
Unknown: d(2,4)
bonne inconnue W:=d(2,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,6},3} qui est  maintenant AA:= - d(3,4)$

Unknown: d(3,4)
Unknown: d(3,4)
bonne inconnue W:=d(3,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,6},4} qui est  maintenant AA:=d(6,6) - d(4,4) + d(0,0)$

Unknowns: {d(6,6),d(4,4),d(0,0)}
Unknowns: {d(6,6),d(4,4),d(0,0)}
bonne inconnue W:=d(6,6)$

sa valeur doit etre WW:=d(4,4) - d(0,0)$

on resout l'equation {{0,6},5} qui est  maintenant AA:= - d(5,4) + d(1,6)$

Unknowns: {d(5,4),d(1,6)}
Unknowns: {d(5,4),d(1,6)}
bonne inconnue W:=d(5,4)$

sa valeur doit etre WW:=d(1,6)$

on resout l'equation {{1,2},0} qui est  maintenant AA:= - d(0,3)$

Unknown: d(0,3)
Unknown: d(0,3)
bonne inconnue W:=d(0,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},1} qui est  maintenant AA:= - d(1,3)$

Unknown: d(1,3)
Unknown: d(1,3)
bonne inconnue W:=d(1,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},2} qui est  maintenant AA:= - d(2,3)$

Unknown: d(2,3)
Unknown: d(2,3)
bonne inconnue W:=d(2,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},3} qui est  maintenant AA:= - d(3,3) + d(2,2) + d(1,
1)$

Unknowns: {d(3,3),d(2,2),d(1,1)}
Unknowns: {d(3,3),d(2,2),d(1,1)}
bonne inconnue W:=d(3,3)$

sa valeur doit etre WW:=d(2,2) + d(1,1)$

on resout l'equation {{1,2},4} qui est  maintenant AA:= - d(4,3) + d(3,2)$

Unknowns: {d(4,3),d(3,2)}
Unknowns: {d(4,3),d(3,2)}
bonne inconnue W:=d(4,3)$

sa valeur doit etre WW:=d(3,2)$

on resout l'equation {{1,2},5} qui est  maintenant AA:= - (d(5,3) + d(3,1) + d(0
,2))$

Unknowns: {d(5,3),d(3,1),d(0,2)}
Unknowns: {d(5,3),d(3,1),d(0,2)}
bonne inconnue W:=d(5,3)$

sa valeur doit etre WW:= - (d(3,1) + d(0,2))$

on resout l'equation {{1,3},4} qui est  maintenant AA:= - d(4,4) + d(2,2) + 2*d(
1,1)$

Unknowns: {d(4,4),d(2,2),d(1,1)}
Unknowns: {d(4,4),d(2,2),d(1,1)}
bonne inconnue W:=d(4,4)$

sa valeur doit etre WW:=d(2,2) + 2*d(1,1)$

on resout l'equation {{1,3},5} qui est  maintenant AA:=d(2,1) - d(1,6)$

Unknowns: {d(2,1),d(1,6)}
Unknowns: {d(2,1),d(1,6)}
bonne inconnue W:=d(1,6)$

sa valeur doit etre WW:=d(2,1)$

on resout l'equation {{1,6},3} qui est  maintenant AA:=d(2,6)$

Unknown: d(2,6)
Unknown: d(2,6)
bonne inconnue W:=d(2,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,6},4} qui est  maintenant AA:=d(3,6) + d(0,1)$

Unknowns: {d(3,6),d(0,1)}
Unknowns: {d(3,6),d(0,1)}
bonne inconnue W:=d(3,6)$

sa valeur doit etre WW:= - d(0,1)$

on resout l'equation {{1,6},5} qui est  maintenant AA:= - d(0,6)$

Unknown: d(0,6)
Unknown: d(0,6)
bonne inconnue W:=d(0,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,3},4} qui est  maintenant AA:= - d(4,5) + d(1,2)$

Unknowns: {d(4,5),d(1,2)}
Unknowns: {d(4,5),d(1,2)}
bonne inconnue W:=d(4,5)$

sa valeur doit etre WW:=d(1,2)$

on resout l'equation {{2,3},5} qui est  maintenant AA:=2*d(2,2) - d(0,0)$

Unknowns: {d(2,2),d(0,0)}
Unknowns: {d(2,2),d(0,0)}
bonne inconnue W:=d(2,2)$

sa valeur doit etre WW:=d(0,0)/2$

on resout l'equation {{2,6},3} qui est  maintenant AA:= - d(2,1)$

Unknown: d(2,1)
Unknown: d(2,1)
bonne inconnue W:=d(2,1)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,6},4} qui est  maintenant AA:=d(0,2)$

Unknown: d(0,2)
Unknown: d(0,2)
bonne inconnue W:=d(0,2)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,6},5} qui est  maintenant AA:= - d(0,1)$

Unknown: d(0,1)
Unknown: d(0,1)
bonne inconnue W:=d(0,1)$

sa valeur doit etre WW:=0$

Derivation equations to cancel (Reduce output) : \\{{{{0,1},0},0},
{{{0,1},1},0},
{{{0,1},2},0},
{{{0,1},3},0},
{{{0,1},4},0},
{{{0,1},5},0},
{{{0,1},6},0},
{{{0,2},3},0},
{{{0,2},4},0},
{{{0,2},5},0},
{{{0,3},4},0},
{{{0,3},5},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,5},4},0},
{{{0,5},5},0},
{{{0,6},0},0},
{{{0,6},1},0},
{{{0,6},2},0},
{{{0,6},3},0},
{{{0,6},4},0},
{{{0,6},5},0},
{{{0,6},6},0},
{{{1,2},0},0},
{{{1,2},1},0},
{{{1,2},2},0},
{{{1,2},3},0},
{{{1,2},4},0},
{{{1,2},5},0},
{{{1,2},6},0},
{{{1,3},0},0},
{{{1,3},1},0},
{{{1,3},2},0},
{{{1,3},3},0},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},0},
{{{1,4},3},0},
{{{1,4},4},0},
{{{1,4},5},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{2,3},0},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},0},
{{{2,3},4},0},
{{{2,3},5},0},
{{{2,3},6},0},
{{{2,4},3},0},
{{{2,4},5},0},
{{{2,5},3},0},
{{{2,5},5},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{4,6},4},0},
{{{5,6},4},0}}$

Il n'y a pas de phase 2$

derivation generique de gtildedelta:$

MATD:=
mat((d(0,0),0,0,0,0,0,0),(0,d(1,1),d(1,2),0,0,0,0),(0,0,d(0,0)/2,0,0,0,0),(d(1,2
),d(3,1),d(3,2),(2*d(1,1) + d(0,0))/2,0,0,0),(d(4,0),d(4,1),d(4,2),d(3,2),(4*d(1
,1) + d(0,0))/2,d(1,2),d(4,6)),(d(5,0),d(5,1),d(5,2), - d(3,1),0,d(1,1) + d(0,0)
,d(5,6)),(d(6,0),2*d(1,2),0,0,0,0,(4*d(1,1) - d(0,0))/2))$
$

pour delta:=

[0  0  0  0  0  0]
[                ]
[0  0  0  0  0  0]
[                ]
[0  0  0  0  0  0]
[                ]
[0  0  0  0  0  1]
[                ]
[1  0  0  0  0  0]
[                ]
[0  0  0  0  0  0]


pour shortformdelta:={0,1,ss,1,0,0,ss,0,0}

Unknowns: {d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,6),
d(4,2),
d(4,1),
d(4,0),
d(3,2),
d(3,1),
d(1,2),
d(1,1),
d(0,0)}
Unknowns: {d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,6),
d(4,2),
d(4,1),
d(4,0),
d(3,2),
d(3,1),
d(1,2),
d(1,1),
d(0,0)}
listeparametresMATD{d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,6),
d(4,2),
d(4,1),
d(4,0),
d(3,2),
d(3,1),
d(1,2),
d(1,1),
d(0,0)}$

dim Der(gtildedelta):=14$

t1:=D(0,0):=

[1  0   0    0    0   0    0   ]
[                              ]
[0  0   0    0    0   0    0   ]
[                              ]
[       1                      ]
[0  0  ---   0    0   0    0   ]
[       2                      ]
[                              ]
[            1                 ]
[0  0   0   ---   0   0    0   ]
[            2                 ]
[                              ]
[                 1            ]
[0  0   0    0   ---  0    0   ]
[                 2            ]
[                              ]
[0  0   0    0    0   1    0   ]
[                              ]
[                          - 1 ]
[0  0   0    0    0   0  ------]
[                          2   ]


Unknowns: {d(5,0),d(4,2),d(3,2),d(1,1),d(0,0)}

Unknowns: {d(5,0),d(4,2),d(3,2),d(1,1),d(0,0)}

t2:=D(1,1):=

[0  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  0  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  2  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  2]


Unknowns: {d(1,1),d(0,0)}
Unknowns: {d(1,1),d(0,0)}
commutant simultane de t1,t2 dans der(gtildedelta):$


mat((d(0,0),0,0,0,0,0,0),(0,d(1,1),0,0,0,0,0),(0,0,d(0,0)/2,0,0,0,0),(0,0,0,(2*d
(1,1) + d(0,0))/2,0,0,0),(0,0,0,0,(4*d(1,1) + d(0,0))/2,0,0),(0,0,0,0,0,d(1,1) +
 d(0,0),0),(0,0,0,0,0,0,(4*d(1,1) - d(0,0))/2))$
$

rank 2 with maximal torus t1,t2

2


matrice de passage de la base X(0)=delta, X(1),..., X(6) a une base  diagonali\
sant le tore maximal: on peut prendre

P:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


P**(-1)*t1*P:=

[1  0   0    0    0   0    0   ]
[                              ]
[0  0   0    0    0   0    0   ]
[                              ]
[       1                      ]
[0  0  ---   0    0   0    0   ]
[       2                      ]
[                              ]
[            1                 ]
[0  0   0   ---   0   0    0   ]
[            2                 ]
[                              ]
[                 1            ]
[0  0   0    0   ---  0    0   ]
[                 2            ]
[                              ]
[0  0   0    0    0   1    0   ]
[                              ]
[                          - 1 ]
[0  0   0    0    0   0  ------]
[                          2   ]

P**(-1)*t2*P:=

[0  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  0  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  2  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  2]


matrice des derivations dans cette base diagonalisante Y(1),...,Y(7):

P**(-1)*MATD*P:=
mat((d(0,0),0,0,0,0,0,0),(0,d(1,1),d(1,2),0,0,0,0),(0,0,d(0,0)/2,0,0,0,0),(d(1,2
),d(3,1),d(3,2),(2*d(1,1) + d(0,0))/2,0,0,0),(d(4,0),d(4,1),d(4,2),d(3,2),(4*d(1
,1) + d(0,0))/2,d(1,2),d(4,6)),(d(5,0),d(5,1),d(5,2), - d(3,1),0,d(1,1) + d(0,0)
,d(5,6)),(d(6,0),2*d(1,2),0,0,0,0,(4*d(1,1) - d(0,0))/2))$
$

PP:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


avec PP:=P*Q:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


MATDDIAGONALISE:=

mat((d(0,0),0,0,0,0,0,0),

    (0,d(1,1),d(1,2),0,0,0,0),

          d(0,0)
    (0,0,--------,0,0,0,0),
            2

                           2*d(1,1) + d(0,0)
    (d(1,2),d(3,1),d(3,2),-------------------,0,0,0),
                                   2

                                  4*d(1,1) + d(0,0)
    (d(4,0),d(4,1),d(4,2),d(3,2),-------------------,d(1,2),d(4,6)),
                                          2

    (d(5,0),d(5,1),d(5,2), - d(3,1),0,d(1,1) + d(0,0),d(5,6)),

                              4*d(1,1) - d(0,0)
    (d(6,0),2*d(1,2),0,0,0,0,-------------------))
                                      2


on voit apparaitre les poids sur la diagonale

r(1) := d(0,0)

r(2) := d(1,1)

         d(0,0)
r(3) := --------
           2

         2*d(1,1) + d(0,0)
r(4) := -------------------
                 2

         4*d(1,1) + d(0,0)
r(5) := -------------------
                 2

r(6) := d(1,1) + d(0,0)

         4*d(1,1) - d(0,0)
r(7) := -------------------
                 2

r(1) := 2*gamma1

r(2) := gamma2

r(3) := gamma1

r(4) := gamma1 + gamma2

r(5) := gamma1 + 2*gamma2

r(6) := 2*gamma1 + gamma2

r(7) :=  - (gamma1 - 2*gamma2)

Le systeme de poids est le systeme 2.29

calcul de relations de commutation de la base diaY(j) diagonalisant le tore

listcommutateursdesx := {{{0,1},x(5)},

   {{0,2},0},

   {{0,3},0},

   {{0,4},0},

   {{0,5},0},

   {{0,6},x(4)},

   {{1,2},x(3)},

   {{1,3},x(4)},

   {{1,4},0},

   {{1,5},0},

   {{1,6},0},

   {{2,3},x(5)},

   {{2,4},0},

   {{2,5},0},

   {{2,6},0},

   {{3,4},0},

   {{3,5},0},

   {{3,6},0},

   {{4,5},0},

   {{4,6},0},

   {{5,6},0}}

diaY(1):=x(0)

diaY(2):=x(1)

diaY(3):=x(2)

diaY(4):=x(3)

diaY(5):=x(4)

diaY(6):=x(5)

diaY(7):=x(6)

liste des commutateurs des diaY(i) :$

listcommutateurdesdiaY:={{{1,2},diay(6)},
{{1,3},0},
{{1,4},0},
{{1,5},0},
{{1,6},0},
{{1,7},diay(5)},
{{2,3},diay(4)},
{{2,4},diay(5)},
{{2,5},0},
{{2,6},0},
{{2,7},0},
{{3,4},diay(6)},
{{3,5},0},
{{3,6},0},
{{3,7},0},
{{4,5},0},
{{4,6},0},
{{4,7},0},
{{5,6},0},
{{5,7},0},
{{6,7},0}}$

Now we make explicit the isomorphism with an algebra of the book:$

Namely g_{7,2.29}$

i.e. we go from the basis diaY(i) to the new basis ZZ(i) defined by the matrix:$

on pose :$

avec comme matrice de changement de base :$


mat((0,0,1,0,0,0,0),(0,2,0,0,0,0,0),(1,0,0,0,0,0,0),(0,0,0,0,-2,0,0),(0,0,0,0,0,
0,-4),(0,0,0,0,0,-2,0),(0,0,0,-4,0,0,0))$
$

det(isom):= -128$

ZZ(1):=diay(3)$

ZZ(2):=2*diay(2)$

ZZ(3):=diay(1)$

ZZ(4):= - 4*diay(7)$

ZZ(5):= - 2*diay(4)$

ZZ(6):= - 2*diay(6)$

ZZ(7):= - 4*diay(5)$

listcommutateursdesZZ:=$

{{1,2},zz(5)}$

{{1,3},0}$

{{1,4},0}$

{{1,5},zz(6)}$

{{1,6},0}$

{{1,7},0}$

{{2,3},zz(6)}$

{{2,4},0}$

{{2,5},zz(7)}$

{{2,6},0}$

{{2,7},0}$

{{3,4},zz(7)}$

{{3,5},0}$

{{3,6},0}$

{{3,7},0}$

{{4,5},0}$

{{4,6},0}$

{{4,7},0}$

{{5,6},0}$

{{5,7},0}$

{{6,7},0}$

We get the commutation relations of$

g_{7,2.29}$

Et cela pour a:=1$

shortformdelta:={0,1,ss,1,0,0,ss,0,0}$

delta:=
mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,1),(1,0,0,0,0,0),(0,0,0
,0,0,0))$
$