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GradedLieAlgebras :: holonomyLie

holonomyLie -- gives the holonomy Lie algebra associated to an arrangement or matroid

Synopsis

Description

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]}}}

See also

Ways to use holonomyLie :