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GradedLieAlgebras :: minPresLie

minPresLie -- gives a minimal presentation up to a specified degree

Synopsis

Description

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]}

See also

Ways to use minPresLie :