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GradedLieAlgebras :: indexFormLie

indexFormLie -- returns an element in the ring representation corresponding to the input

Synopsis

Description

The output of indexFormLie uses basis elements for the Lie algebra which are indexed variables with two indices, the first degree and a number, see mbRing and How to write Lie elements.

i1 : L = lieAlgebra( {a,b}, {})

o1 = L

o1 : LieAlgebra
i2 : b3=basisLie 3

o2 = {[a, b, a], [b, b, a]}

o2 : List
i3 : indexFormLie b3_0

o3 = mb
       {3, 0}

o3 : QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}
i4 : defLie oo

o4 = [a, b, a]

o4 : Array
i5 : indexFormLie([b,a,b])

o5 = -mb
        {3, 1}

o5 : QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}
i6 : defLie oo

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

o6 : List
i7 : indexFormLie{oo,[a],[a,b]}

o7 = {-mb      , mb      , -mb      }
         {3, 1}    {1, 0}     {2, 0}

o7 : List

See also

Ways to use indexFormLie :