Question: Interpret this output From the Lie Algebra/Differential Geometry Package

So I am doing some algebra calculations with what I thought were Lie Algebras.   It looks like

> with(DifferentialGeometry); with(LieAlgebras);
> StructureEquations := [[a, b] = -f+e, [a, c] = -f+d, [c, b] = -f+e, [d, e] = p*d+q*e+r*f, [e, f] = p*d+q*e+r*f, [d, f] = p*d+q*e+r*f, [a, d] = q*a+p*b, [a, f] = r*c-p*b, [a, e] = -q*a+p*b, [c, d] = q*a+p*b, [c, f] = r*c-p*b, [c, e] = -q*a+p*b, [b, d] = q*a+p*b, [b, f] = r*c-p*b, [b, e] = -q*a+p*b];
[[a, b] = -f + e, [a, c] = -f + d, [c, b] = -f + e, [d, e] = p d + q e + r f,

  [e, f] = p d + q e + r f, [d, f] = p d + q e + r f, [a, d] = q a + p b,

  [a, f] = r c - p b, [a, e] = -q a + p b, [c, d] = q a + p b,

  [c, f] = r c - p b, [c, e] = -q a + p b, [b, d] = q a + p b,

  [b, f] = r c - p b, [b, e] = -q a + p b]
> L := LieAlgebraData(StructureEquations, [a, b, c, d, e, f], algebra5);
 

where my structure constants are p, q, and r.  I was suprised to find that this is not in fact a lie algebra. Using the query command I discovered p,q,r are subject to:

{p, q, -p, 2*p, -q, 2*q, -r, 2*r, -p^2, -r^2, -p-q, -p+q, p-q, p+q, p-r, 2*p+q, -2*q+p, 2*q-p, -2*r+p, -r-p, r+q, 2*r-q, 3*r-p, q^2-3*q*p, q^2-q*r, -2*q*p-p^2, -q+r-p, q+p-r, r+p-q, q^2-2*q*p+q*r, -r^2+p*r-q*r, -r^2+p*r+q*r, p*r+q*p-p^2}

(this is the first arguement of Query({p,q,r},"Jacobi")

My question is what exactly is this system?  I'm not sure how to interpret this.

Thanks so much

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