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GradedLieAlgebras :: multListLie

multListLie -- Lie multiplication of lists of LieElement

Synopsis

Description

It is also possible to use the infix operator SPACE to multiply two lists in the case there is no option defined.

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

There is an option multOnly which only multiplies those pairs (x,y) for which multOnly(x,y) is true.

i6 : apply(b2,weightLie)

o6 = {{2, 2, 0}, {2, 3, 0}}

o6 : List
i7 : apply(b3,weightLie)

o7 = {{3, 4, 0}, {3, 5, 0}}

o7 : List
i8 : multListLie(b2,b3,multOnly=>(x,y)->
       ((weightLie x)_1 === 3 and (weightLie y)_1 === 5))

o8 = { - (1/2)(b a b b a) + (1/4)(b b b a a)}

o8 : List
i9 : indexFormLie oo

      1           1
o9 = {-mb       - -mb      }
      4  {5, 1}   2  {5, 2}

o9 : List

See also

Ways to use multListLie :