The list I is extended by the action on I of the differential in L. The program converts the elements in the list, so that they will have type M=ambient(L) instead. The list of these converted elements may be looked upon by writing Q.relsLie.
i1 : M = lieAlgebra({a,b,c}) o1 = M o1 : LieAlgebra |
i2 : L = M/{a b} o2 = L o2 : LieAlgebra |
i3 : Q = L/{a c} o3 = Q o3 : LieAlgebra |
i4 : peekLie Q o4 = gensLie => {a, b, c} genWeights => {{1, 0}, {1, 0}, {1, 0}} genSigns => {0, 0, 0} relsLie => { - (b a), - (c a)} genDiffs => {0, 0, 0} field => QQ diffl => false compdeg => 1 |
i5 : ambient Q o5 = M o5 : LieAlgebra |
i6 : class (Q.relsLie)_0 o6 = M o6 : LieAlgebra |
The Lie algebra Q below is M modulo the ideal in M generated by the elements in Q.relsLie and with differential defined by the induced differential on L.
i7 : L = lieAlgebra({a,b,c2,c3},genWeights=>{{1,0},{1,0},{2,1},{3,2}}, genSigns=>{1,1,1,1},diffl=>true) o7 = L o7 : LieAlgebra |
i8 : L = diffLieAlgebra{L.zz,L.zz,a a,b c2}/{a c2} warning: relations have been added for the square of the differential to be zero o8 = L o8 : LieAlgebra |
i9 : Q = L/{b c3} warning: new generators for the ideal have been added to get invariance of the differential o9 = Q o9 : LieAlgebra |
i10 : peekLie Q o10 = gensLie => {a, b, c2, c3} genWeights => {{1, 0}, {1, 0}, {2, 1}, {3, 2}} genSigns => {1, 1, 1, 1} relsLie => { - (b a a), (a c2), (b c3), - (b b c2)} genDiffs => {0, 0, (a a), (b c2)} field => QQ diffl => true compdeg => 0 |
i11 : M = ambient Q o11 = M o11 : LieAlgebra |
i12 : peekLie M o12 = gensLie => {a, b, c2, c3} genWeights => {{1, 0}, {1, 0}, {2, 1}, {3, 2}} genSigns => {1, 1, 1, 1} relsLie => {} genDiffs => {0, 0, 0, 0} field => QQ diffl => true compdeg => 4 |