This is an option to tell lieAlgebra to assign the given weights to the generators. A weight is a list of integers of a length, which is the same for all generators. The first degree (also just called the degree), see degLie, is positive and, if the Lie algebra has a differential (i.e., the option diffl is true), the last degree is the homological degree, which is non-negative and less than the first degree. If the Lie algebra has no differential (i.e., the option diffl is false), the program defines a differential to be 0 and adds a last degree 0 to the existing degrees. When the option is given as a list of integers n1,n2,..., which is not possible when the option diffl is true, then the program defines the weights for the generators to be {n1,0}, {n2,0},... . The default value is 1, which has the effect that all generators have degree {1,0}.
i1 : peekLie lieAlgebra({a,b},genWeights=>{{1,2},{2,3}}) o1 = gensLie => {a, b} genWeights => {{1, 2, 0}, {2, 3, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => false compdeg => 0 |
i2 : peekLie lieAlgebra({a,b},genWeights=>{{2,1},{3,2}},diffl=>true) o2 = gensLie => {a, b} genWeights => {{2, 1}, {3, 2}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => true compdeg => 0 |
i3 : peekLie lieAlgebra({a,b}) o3 = gensLie => {a, b} genWeights => {{1, 0}, {1, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => false compdeg => 0 |
i4 : peekLie lieAlgebra({a,b},genWeights=>{{1,0},{1,0}}) o4 = gensLie => {a, b} genWeights => {{1, 0, 0}, {1, 0, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => false compdeg => 0 |
i5 : peekLie lieAlgebra({a,b},genWeights=>{{1,0},{1,0}},diffl=>true) o5 = gensLie => {a, b} genWeights => {{1, 0}, {1, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => true compdeg => 0 |
i6 : peekLie lieAlgebra({a,b},genWeights=>{1,2}) o6 = gensLie => {a, b} genWeights => {{1, 0}, {2, 0}} genSigns => {0, 0} relsLie => {} genDiffs => {0, 0} field => QQ diffl => false compdeg => 0 |