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 |
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]} |