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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 current 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},genWeights=>{1,1,1,2,2,3})/
      {e12 e34,e12 e13,e12 e14,
       e23 e13,e23 e24,e23 e14,
       e34 e24,e34 e14,e13 e24,
       e13 e14,e24 e14,
       e12 e23 - e13,
       e12 e24 - e14,
       e13 e34 - e14,
       e23 e34 - e24}

o1 = L

o1 : LieAlgebra
i2 : M=minPresLie 3

o2 = M

o2 : LieAlgebra
i3 : peekLie M

o3 = gensLie => {e12, e23, e34}
     genWeights => {{1, 0}, {1, 0}, {1, 0}}
     genSigns => {0, 0, 0}
     relsLie => {(e34 e12), (e34 e34 e23), (e23 e34 e23), (e23 e23 e12), (e12 e23 e12)}
     genDiffs => {0, 0, 0}
     field => QQ
     diffl => false
     compdeg => 1
i4 : dimsLie 4

o4 = {3, 2, 1, 0}

o4 : List

See also

Ways to use minPresLie :