The ring representation of the Lie algebra L may be obtained as L.cache.mbRing. Its generators constitute a basis for L. In order to transform a general Lie expression, generalExpressionLie, to a linear polynomial in L.cache.mbRing, use indexFormLie. For the other direction, use defLie, see also How to write Lie elements.
i1 : L=lieAlgebra({a,b,c},{[a,b]}) o1 = L o1 : LieAlgebra |
i2 : indexFormLie{{1,2},{[a,c],[b,c]}} o2 = - mb - 2mb {2, 0} {2, 1} o2 : QQ[mb , mb , mb , mb , mb ] {1, 0} {1, 1} {1, 2} {2, 0} {2, 1} |
i3 : defLie oo o3 = {{-1, -2}, {[c, a], [c, b]}} o3 : List |
i4 : L.cache.mbRing o4 = QQ[mb , mb , mb , mb , mb ] {1, 0} {1, 1} {1, 2} {2, 0} {2, 1} o4 : PolynomialRing |