The ring is used as a representation of the Lie algebra $L$ and may be obtained as L#cache.mbRing. The ring mbRing is very large: it has as many generators as the total dimension of the computed Lie algebra. For this reason, you should give the ring a name to avoid a large output. In order to transform a Lie element to a linear polynomial in L#cache.mbRing, use indexForm. For the other direction, use standardForm(RingElement,LieAlgebra).
i1 : L=lieAlgebra{a,b,c}/{a b-a c}
o1 = L
o1 : LieAlgebra
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i2 : dims(1,5,L)
o2 = {3, 2, 5, 10, 24}
o2 : List
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i3 : R=L#cache.mbRing o3 = R o3 : PolynomialRing |
i4 : numgens R o4 = 44 |
i5 : indexForm(a a a a b+a a a b c)
o5 = - mb - mb + mb
{5, 0} {5, 1} {5, 2}
o5 : R
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i6 : standardForm(oo,L) o6 = - (a a a c a) - (b a a c a) + (c a a c a) o6 : L |
i7 : a a a a b+a a a b c o7 = - (a a a c a) - (b a a c a) + (c a a c a) o7 : L |