characterLie -- computes the trace of a Lie representation

Synopsis

• Usage:

  r = characterLie(d,x,y)

• Inputs:

  • d, an integer, the degree
  • x, a list, a permutation (a list of cycles) which operates on y
  • y, a list, general Lie expressions, generalExpressionLie, of degree d defining a basis for a subspace in degree d
• Outputs:

  • r, a ring element, the trace for the representation defined by permuting the generators by x

Description

i1 : L=lieAlgebra({a,b,c},{}, field=>ZZ/31)

o1 = L

o1 : LieAlgebra

i2 : basisLie 3

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

o2 : List

i3 : characterLie(3,{{a,b,c}}, basisLie(3))

o3 = -1

     ZZ
o3 : --
     31

i4 : permopLie({{a,b,c}},[c,b,a])

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

o4 : List

i5 : permopLie({{a,b,c}},[b,c,a])

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

o5 : List

See also

• permopLie -- the result of a permutation operating on a general Lie expression
• symmPermLie -- checks if a permutation of the generators is an automorphism
• symmCyclePermLie -- checks if a permutation of the generators in the form of cycles is an automorphism