def L6_32(F, a):
sc = {
('X_1', 'X_2'): {
'X_3': 1
},
('X_1', 'X_3'): {
'X_4': 1
},
('X_1', 'X_4'): {
'X_5': 1
},
('X_2', 'X_3'): {
'X_6': a
},
('X_2', 'X_5'): {
'X_6': 1
},
('X_3', 'X_4'): {
'X_6': 1
}
}
return ClassifiedNilpotentLieAlgebra(
F,
'L6_32(%s)' % (a),
sc,
names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L6_21(F, a):
# classification in GAP follows Cicalo-de Graaf-Schneider 2012
# instead of the slightly different de Graaf 2007
# the only differences are:
# L6_19(0) -> L6_27
# L6_21(0) -> L6_28
if a == F.zero():
return L6_28(F)
sc = {
('X_1', 'X_2'): {
'X_3': 1
},
('X_1', 'X_3'): {
'X_4': 1
},
('X_1', 'X_4'): {
'X_6': 1
},
('X_2', 'X_3'): {
'X_5': 1
},
('X_2', 'X_5'): {
'X_6': a
}
}
return ClassifiedNilpotentLieAlgebra(
F,
'L6_21(%s)' % (a),
sc,
names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L5_8(F):
sc = {
('X_1', 'X_2'): {'X_4': 1},
('X_1', 'X_3'): {'X_5': 1}
}
return ClassifiedNilpotentLieAlgebra(F, 'L5_8', sc,
names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5'])
def L6_27(F):
sc = {
('X_1', 'X_2'): {
'X_3': 1
},
('X_1', 'X_3'): {
'X_5': 1
},
('X_2', 'X_4'): {
'X_6': 1
}
}
return ClassifiedNilpotentLieAlgebra(
F, 'L6_27', sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L6_1(F):
sc = {}
return ClassifiedNilpotentLieAlgebra(
F, 'L6_1', sc, names=['X_1', 'X_2', 'X_3', 'X_4', 'X_5', 'X_6'])
def L1_1(F):
sc = {}
return ClassifiedNilpotentLieAlgebra(F, 'L1_1', sc, names=['X_1'])
def L3_2(F):
sc = {('X_1', 'X_2'): {'X_3': 1}}
return ClassifiedNilpotentLieAlgebra(F,
'L3_2',
sc,
names=['X_1', 'X_2', 'X_3'])
