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GradedLieAlgebras :: characterLie

characterLie -- computes the trace of a Lie representation

Synopsis

Description

The permutation x of the generators is given as a list of cycles. The subspace of L in degree d, generated by the elements in y, should be invariant under x and the output characterLie(d,x,y) gives the trace of x as an element in L.field.

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

Ways to use characterLie :