LieAlgebra * LieAlgebra -- free product of Lie algebras

Synopsis

Operator: *
Usage:

M = L1*L2
Inputs:
- L1, an instance of the type LieAlgebra
- L2, an instance of the type LieAlgebra
Outputs:
- M, an instance of the type LieAlgebra, the free product of $L1$ and $L2$

Description

i1 : F1 = lieAlgebra({a,b},Signs=>{0,1},Weights=>{{2,0},{2,1}},
         LastWeightHomological=>true)

o1 = F1

o1 : LieAlgebra

i2 : L1 = differentialLieAlgebra{0_F1,a}

o2 = L1

o2 : LieAlgebra

i3 : F2 = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
         Signs=>{1,1,1},LastWeightHomological=>true)

o3 = F2

o3 : LieAlgebra

i4 : L2 = differentialLieAlgebra{0_F2,a a,a b}/{b b+4 a c}

o4 = L2

o4 : LieAlgebra

i5 : M = L1*L2

o5 = M

o5 : LieAlgebra

i6 : describe(M)

o6 = generators => {pr , pr , pr , pr , pr }
                      0    1    2    3    4
     Weights => {{2, 0}, {2, 1}, {1, 0}, {2, 1}, {3, 2}}
     Signs => {0, 1, 1, 1, 1}
     ideal => { - (pr_2 pr_2 pr_2), (pr_3 pr_3) + 4 (pr_2 pr_4), (pr_2 pr_2 pr_3) + (pr_2 pr_2 pr_3) - (pr_3 pr_2 pr_2) - 4 (pr_2 pr_2 pr_3)}
     ambient => LieAlgebra{...10...}
     diff => {0, pr_0, 0, (pr_2 pr_2), (pr_2 pr_3)}
     Field => QQ
     computedDegree => 0

i7 : normalForm\ideal(M)

o7 = {0, (pr_3 pr_3) + 4 (pr_2 pr_4), 0}

o7 : List

i8 : d = differential M

o8 = d

o8 : LieDerivation

i9 : d (pr_1 pr_3)

o9 =  - (pr_3 pr_0) + 2 (pr_2 pr_2 pr_1)

o9 : M