lieSubSpace -- make a Lie subspace

Synopsis

• Usage:

  S=lieSubSpace(gens)

• Inputs:
  • gens, a list, a list of homogeneous elements in a Lie algebra $L$
• Outputs:
  • S, an instance of the type LieSubSpace, the subspace of $L$ generated by the list gens

Description

i1 : F=lieAlgebra({a,b,c,r3,r4,r42},
        Weights => {{1,0},{1,0},{2,0},{3,1},{4,1},{4,2}},
        Signs=>{0,0,0,1,1,0},LastWeightHomological=>true)

o1 = F

o1 : LieAlgebra

i2 : D=differentialLieAlgebra{0_F,0_F,0_F,a c,a a c,r4 - a r3}

o2 = D

o2 : LieAlgebra

i3 : S=lieSubSpace{b c - a c,a b,b r4 - a r4}

o3 = S

o3 : LieSubSpace

i4 : describe S

o4 = generators => { - (a c) + (b c),  - (b a),  - (a r4) + (b r4)}
     lieAlgebra => D

i5 : d=differential D

o5 = d

o5 : LieDerivation

i6 : basis(5,S)

o6 = {(a r4) - (b r4)}

o6 : List

i7 : d\oo

o7 = {(a a a c) - (b a a c)}

o7 : List

See also

• lieAlgebra -- make a free Lie algebra
• lieSubAlgebra -- make a Lie subalgebra
• lieIdeal -- make a Lie ideal