This constructs the holonomy Lie algebra of an arrangement or matroid given by the set of 2-flats. Input may be any set of subsets of a finite set, such that all subsets have at most one element in common and are of length at least three. Indeed, for any such set of subsets there is a unique simple matroid of rank at most three with the given set as the set of 2-flats of size at least three.
i1 : L=holonomyLie({{0,1,2,3}}) o1 = L o1 : LieAlgebra |
i2 : peek L o2 = LieAlgebra{cache => CacheTable{...10...} } compdeg => 0 deglength => 2 field => QQ genDiffs => {[], [], [], []} genSigns => {0, 0, 0, 0} gensLie => {0, 1, 2, 3} genWeights => {{1, 0}, {1, 0}, {1, 0}, {1, 0}} numGen => 4 relsLie => {{{1, 1, 1, 1}, {[1, 0], [1, 1], [1, 2], [1, 3]}}, {{1, 1, 1, 1}, {[2, 0], [2, 1], [2, 2], [2, 3]}}, {{1, 1, 1, 1}, {[3, 0], [3, 1], [3, 2], [3, 3]}}} |