A minimal set of generators and relations for the Lie algebra L (without differential) is given. In general the presentation applies to H0(L). The example L below is the Lie algebra of strictly upper triangular 4x4-matrices given by its multiplication table on the natural basis.
i1 : L=lieAlgebra({e12,e23,e34,e13,e24,e14},
{[e12,e34],[e12,e13],[e12,e14],
[e23,e13],[e23,e24],[e23,e14],[e34,e24],[e34,e14],
[e13,e24],[e13,e14],
[e24,e14],
{{1,-1},{[e12,e23],[e13]}},{{1,-1},{[e12,e24],[e14]}},
{{1,-1},{[e13,e34],[e14]}},
{{1,-1},{[e23,e34],[e24]}}},
genWeights=>{1,1,1,2,2,3})
o1 = L
o1 : LieAlgebra
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i2 : M=minPresLie 3 o2 = M o2 : LieAlgebra |
i3 : peek M
o3 = LieAlgebra{cache => CacheTable{...9...} }
compdeg => 0
deglength => 2
field => QQ
genDiffs => {[], [], []}
genSigns => {0, 0, 0}
gensLie => {e12, e23, e34}
genWeights => {{1, 0}, {1, 0}, {1, 0}}
numGen => 3
relsLie => {[e34, e12], [e34, e34, e23], [e23, e34, e23], [e23, e23, e12], [e12, e23, e12]}
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