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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 identity is written {{}}. The permutation should define an automorphism on L. The subspace of L in degree d, generated by the elements in y, should be invariant under x and the output characterLie(x,y) gives the trace of x, which is 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({{a,b,c}}, basisLie(3))

o3 = -1

     ZZ
o3 : --
     31
i4 : permopLie({{a,b,c}},c b a)

o4 = (b c a) - (c b a)

o4 : L
i5 : permopLie({{a,b,c}},b c a)

o5 =  - (c b a)

o5 : L

See also

Ways to use characterLie :