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GradedLieAlgebras :: List List

List List -- Lie multiplication of lists or multiplication in the Ext-algebra of lists

Synopsis

Description

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

See also