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GradedLieAlgebras :: degLie

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

Synopsis

Description

The degLie of L.zz, the zero element in L, is defined to be 0.

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

o1 = L

o1 : LieAlgebra
i2 : degLie(a)

o2 = 1
i3 : degLie 0

o3 = 1
i4 : degLie L.zz

o4 = 0
i5 : degLie(a a c)

o5 = 4
i6 : g = a c - b c

o6 = (a c) - (b c)

o6 : L
i7 : degLie g

o7 = 3
i8 : m=indexFormLie g

o8 = mb       - mb
       {3, 2}     {3, 3}

o8 : QQ[mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {2, 1}    {3, 0}    {3, 1}    {3, 2}    {3, 3}    {4, 0}    {4, 1}    {4, 2}    {4, 3}    {4, 4}    {4, 5}    {4, 6}
i9 : (degree m)_0

o9 = 3
i10 : degLie {L.zz,b b,c - 2 a b}

o10 = {0, 0, 2}

o10 : List
i11 : d = derLie{a b,c,L.zz}

o11 = d

o11 : DerLie
i12 : degLie d

o12 = 1

See also

Ways to use degLie :