A generator may be of class Symbol or IndexedVariable. The same name for a generator can be used in several Lie algebras and also as name for a variable in a polynomial ring. Relations are introduced by the operator /, see LieAlgebra / List. A differential Lie algebra is defined by giving the value of the differential on the generators, see diffLieAlgebra. Lie multiplication is given by LieElement LieElement. The zero Lie algebra is defined as lieAlgebra{}.
i1 : L1 = lieAlgebra{a,b}/{a a b - b b a, a a a a b} o1 = L1 o1 : LieAlgebra |
i2 : dimsLie 6 o2 = {2, 1, 1, 1, 1, 0} o2 : List |
i3 : peekLie L1 o3 = gensLie => {a, b} genWeights => {{1, 0}, {1, 0}} genSigns => {0, 0} relsLie => { - (a b a) - (b b a), - (a a a b a)} genDiffs => {0, 0} field => QQ diffl => false compdeg => 6 |
i4 : F2 = lieAlgebra({a,b,c},genWeights=>{{1,0},{1,0},{2,1}}, genSigns=>{1,1,1},diffl=>true) o4 = F2 o4 : LieAlgebra |
i5 : L2 = diffLieAlgebra{F2.zz,F2.zz,a a + b b}/{a b,a c} o5 = L2 o5 : LieAlgebra |
i6 : peekLie L2 o6 = gensLie => {a, b, c} genWeights => {{1, 0}, {1, 0}, {2, 1}} genSigns => {1, 1, 1} relsLie => {(b a), (a c)} genDiffs => {0, 0, (a a) + (b b)} field => QQ diffl => true compdeg => 3 |
i7 : dimTableLie 5 o7 = | 2 2 0 0 0 | | 0 1 1 1 1 | | 0 0 0 1 1 | | 0 0 0 0 0 | | 0 0 0 0 0 | 5 5 o7 : Matrix ZZ <--- ZZ |
i8 : peekLie lieAlgebra{} o8 = gensLie => {} genWeights => {} genSigns => {} relsLie => {} genDiffs => {} field => QQ diffl => false compdeg => 0 |