In the example below, ExtUL(QQ,QQ) is equal to R and a basis as a vector space is given by the generators of the ring representation L.cache.extAlgRing, see extAlgRing.
i1 : R=QQ[x,y,z, SkewCommutative=>{x,y,z}] o1 = R o1 : PolynomialRing |
i2 : L=koszulDualLie(R) o2 = L o2 : LieAlgebra |
i3 : extAlgLie 3 o3 = | 3 0 0 | | 0 3 0 | | 0 0 1 | 3 3 o3 : Matrix ZZ <--- ZZ |
i4 : L.cache.extAlgRing o4 = QQ[ext , ext , ext , ext , ext , ext , ext ] 0 1 2 3 4 5 6 o4 : PolynomialRing |
i5 : m=extAlgMultLie(ext_1,ext_2) o5 = -ext 3 o5 : QQ[ext , ext , ext , ext , ext , ext , ext ] 0 1 2 3 4 5 6 |
i6 : extAlgMultLie(ext_0,m) o6 = ext 6 o6 : QQ[ext , ext , ext , ext , ext , ext , ext ] 0 1 2 3 4 5 6 |