next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: localLie

localLie -- gives the Lie algebra and a basis for a local subalgebra of the holonomy Lie algebra of an arrangement or matroid

Synopsis

Description

The generators in the ith 2-flat (beginning with i=0) in the input for holonomyLie generate a subalgebra of the holonomy Lie algebra and the output of localLie(i,n) is a basis for this subalgebra in the specified degree n. The output of localLie(i) is the Lie algebra itself.

i1 : L=holonomyLie({{0,1,2},{0,3,4},{1,3,5},{2,4,5}})

o1 = L

o1 : LieAlgebra
i2 : peek localLie(2)

o2 = LieAlgebra{cache => CacheTable{...10...}                                                            }
                compdeg => 0
                deglength => 2
                field => QQ
                genDiffs => {[], [], []}
                genSigns => {0, 0, 0}
                gensLie => {1, 3, 5}
                genWeights => {{1, 0}, {1, 0}, {1, 0}}
                numGen => 3
                relsLie => {{{1, 1, 1}, {[3, 1], [3, 3], [3, 5]}}, {{1, 1, 1}, {[5, 1], [5, 3], [5, 5]}}}
i3 : localLie(2,3)

o3 = {[3, 5, 3], [5, 5, 3]}

o3 : List

See also

Ways to use localLie :