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GradedLieAlgebras :: degLie

degLie -- the first degree of a graded element in the LieAlgebra

Synopsis

Description

The degLie of [] is defined to be 0. However, the degree of [] should be thought of as arbitrary since, in the example below, the element [b,b] has degLie 2 and is equal to [] in L.

i1 : L=lieAlgebra({a,b,c},{},genWeights => {{1,1},{1,1},{2,2}})

o1 = L

o1 : LieAlgebra
i2 : degLie(a)

o2 = 1
i3 : degLie([a,a,c])

o3 = 4
i4 : g={{1,-1},{[a,c],[b,c]}}

o4 = {{1, -1}, {[a, c], [b, c]}}

o4 : List
i5 : degLie g

o5 = 3
i6 : m=indexFormLie g

o6 = mb       - mb
       {3, 2}     {3, 3}

o6 : QQ[mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {2, 1}    {3, 0}    {3, 1}    {3, 2}    {3, 3}
i7 : (degree m)_0

o7 = 3
i8 : degLie {[],[b,b],{{1,2},{[c],[a,b]}}}

o8 = {0, 2, 2}

o8 : List

See also

Ways to use degLie :