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GradedLieAlgebras :: LieAlgebra ** LieAlgebra

LieAlgebra ** LieAlgebra -- Direct sum of Lie algebras

Synopsis

Description

i1 : L1 = lieAlgebra({a,b},genSigns=>{0,1},genWeights=>{{2,0},{2,1}},
          diffl=>true)

o1 = L1

o1 : LieAlgebra
i2 : L1 = diffLieAlgebra{L1.zz,a}

o2 = L1

o2 : LieAlgebra
i3 : L2 = lieAlgebra({a,b,c},genWeights=>{{1,0},{2,1},{3,2}},
         genSigns=>{1,1,1},diffl=>true)

o3 = L2

o3 : LieAlgebra
i4 : L2 = diffLieAlgebra{L2.zz,a a,a b}/{b b+4 a c}

o4 = L2

o4 : LieAlgebra
i5 : S = L1**L2

o5 = S

o5 : LieAlgebra
i6 : peekLie(S)

o6 = gensLie => {pr , pr , pr , pr , pr }
                   0    1    2    3    4
     genWeights => {{2, 0}, {2, 1}, {1, 0}, {2, 1}, {3, 2}}
     genSigns => {0, 1, 1, 1, 1}
     relsLie => {(pr_3 pr_3) + 4 (pr_2 pr_4), (pr_2 pr_0), (pr_3 pr_0),  - (pr_0 pr_4),  - (pr_2 pr_1),  - (pr_3 pr_1),  - (pr_1 pr_4)}
     genDiffs => {0, pr_0, 0, (pr_2 pr_2), (pr_2 pr_3)}
     field => QQ
     diffl => true
     compdeg => 5