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quotient(LieIdeal,FGLieSubAlgebra) -- make the quotient of a Lie ideal by a finitely generated Lie subalgebra



The optional inputs given above are not relevant for Lie algebras. A Lie element $x$ is in $T$ if $x$ multiplies all the generators of $S$ into $I$. However, $T$ is not in general finitely generated.

i1 : L=lieAlgebra{a,b,c}/{a a b-c c b,b b a-b b c}

o1 = L

o1 : LieAlgebra
i2 : I=lieIdeal{a}

o2 = I

o2 : FGLieIdeal
i3 : S=lieSubAlgebra{b,c}

o3 = S

o3 : FGLieSubAlgebra
i4 : K=quotient(I,S)

o4 = K

o4 : LieSubAlgebra
i5 : basis(2,K)

o5 = {(b a), (c a), (c b)}

o5 : List

See also

Ways to use this method: