The generators in the ith set (beginning with i=0) in the inputs of holonomyLie generate a subalgebra of the holonomy Lie algebra and the output of localLie(i) is this Lie subalgebra. If the set is of size k, then the local Lie algebra is free on k generators if the set belongs to the first input set and it is free on k-1 generators in degree >=2 if it belongs to the second input set.
i1 : L=holonomyLie({{a1,a2},{a3,a4}},{{a1,a3,a5},{a2,a4,a5}}) o1 = L o1 : LieAlgebra |
i2 : peekLie localLie(1) o2 = gensLie => {a3, a4} genWeights => {{1, 0}, {1, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => false compdeg => 0 |
i3 : peekLie localLie(2) o3 = gensLie => {a1, a3, a5} genWeights => {{1, 0}, {1, 0}, {1, 0}} genSigns => {0, 0, 0} relsLie => {(a3 a1) - (a5 a3), (a5 a1) + (a5 a3)} genDiffs => {0, 0, 0} field => QQ diffl => false compdeg => 0 |