next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: multListLie

multListLie -- Lie multiplication of lists of general Lie expressions

Synopsis

Description

i1 : L = lieAlgebra( {a,b}, {[a,a,a,b]},genWeights => {{1,1},{1,2}},
         genSigns=>{1,0})

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 : multListLie(b2,b3)

                                                                    1  1
o4 = {[], {{-1}, {[a, b, b, a, a]}}, {{-1}, {[a, b, b, a, a]}}, {{- -, -},
                                                                    2  4
     ------------------------------------------------------------------------
     {[b, a, b, b, a], [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)

          1  1
o8 = {{{- -, -}, {[b, a, b, b, a], [b, b, b, a, a]}}}
          2  4

o8 : List
i9 : indexFormLie oo

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

o9 : List

See also

Ways to use multListLie :