It is also possible to use the prefix operator multListLie to multiply two lists of LieElement. In the case of lists of RingElement, the elements should belong to the polynomial ring L.cache.extRepRing, see extRepRing. In this case it is also possible to use the prefix operator extMultLie
i1 : L = lieAlgebra( {a,b},genWeights => {{1,1},{1,2}}, genSigns=>{1,0})/{a a a b} o1 = L o1 : LieAlgebra |
i2 : b2 = basisLie 2 o2 = {(a a), (b a)} o2 : List |
i3 : b3 = basisLie 3 o3 = {(b a a), (b b a)} o3 : List |
i4 : b2 b3 o4 = {0, - (a b b a a), - (a b b a a), - (1/2)(b a b b a) + (1/4)(b b b a ------------------------------------------------------------------------ a)} o4 : List |
i5 : indexFormLie oo 1 1 o5 = {0, -mb , -mb , -mb - -mb } {5, 0} {5, 0} 4 {5, 1} 2 {5, 2} o5 : List |
i6 : M=lieAlgebra({a,b},genSigns=>1)/{a a,a b} o6 = M o6 : LieAlgebra |
i7 : extTableLie 3 o7 = | 2 0 0 | | 0 2 0 | | 0 0 2 | 3 3 o7 : Matrix ZZ <--- ZZ |
i8 : {ext_0,ext_1,ext_2} {ext_3} o8 = {ext , ext , 0} 4 5 o8 : List |