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GradedLieAlgebras :: multLie

multLie -- Lie multiplication of two general Lie expression elements

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 : b4 = basisLie 4

o4 = {[b, b, a, a], [a, b, b, a], [b, b, b, a]}

o4 : List
i5 : m1=multLie([a],b4_1)

         1
o5 = {{- -}, {[a, b, b, a, a]}}
         2

o5 : List
i6 : m2=multLie([b],m1)

         1
o6 = {{- -}, {[b, a, b, b, a, a]}}
         2

o6 : List
i7 : m3=multLie(m1,m2)

       1    1
o7 = {{-, - -}, {[b, a, a, b, a, b, a, b, b, a, a], [b, a, b, a, a, b, a, b,
       4    4
     ------------------------------------------------------------------------
     b, a, a]}}

o7 : List
i8 : S=L.cache.mbRing

o8 = S

o8 : PolynomialRing
i9 : i1=indexFormLie m1

       1
o9 = - -mb
       2  {5, 0}

o9 : S
i10 : i2=indexFormLie m2

        1
o10 = - -mb
        2  {6, 0}

o10 : S
i11 : i3=indexFormLie m3

        1            1
o11 = - -mb        + -mb
        4  {11, 1}   4  {11, 4}

o11 : S

See also

Ways to use multLie :