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GradedLieAlgebras :: mbRing

mbRing -- the ring representation of the Lie algebra used as output

Synopsis

Description

The ring representation of the Lie algebra L may be obtained as L.cache.mbRing. Its generators constitute a basis for L. In order to transform a general Lie expression, generalExpressionLie, to a linear polynomial in L.cache.mbRing, use indexFormLie. For the other direction, use defLie, see also How to write Lie elements.

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

o1 = L

o1 : LieAlgebra
i2 : indexFormLie{{1,2},{[a,c],[b,c]}}

o2 = - mb       - 2mb
         {2, 0}      {2, 1}

o2 : QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {1, 2}    {2, 0}    {2, 1}
i3 : defLie oo

o3 = {{-1, -2}, {[c, a], [c, b]}}

o3 : List
i4 : L.cache.mbRing

o4 = QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {1, 2}    {2, 0}    {2, 1}

o4 : PolynomialRing

See also

For the programmer

The object mbRing is a symbol.