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GradedLieAlgebras :: basis(List,VectorSpace)

basis(List,VectorSpace) -- compute a basis

Synopsis

Description

The optional inputs given above are not relevant for Lie algebras.

i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
           Signs=>{1,1,1},LastWeightHomological=>true)

o1 = L

o1 : LieAlgebra
i2 : D= differentialLieAlgebra({0_L,a a,a b})

o2 = D

o2 : LieAlgebra
i3 : J=lieIdeal({b b + 4 a c})

o3 = J

o3 : FGLieIdeal
i4 : Q=D/J

o4 = Q

o4 : LieAlgebra
i5 : H=lieHomology Q

o5 = H

o5 : VectorSpace
i6 : basis({5,3},H)

o6 = {(b c)}

o6 : List
i7 : Z=cycles Q

o7 = Z

o7 : LieSubAlgebra
i8 : basis({5,3},Z)

o8 = {(b c)}

o8 : List

See also