trace(ZZ,LieSubSpace,LieAlgebraMap) -- compute the trace of a Lie algebra map acting on a Lie subspace

Synopsis

Function: trace
Usage:

r = trace(n,S,f)
Inputs:
- n, an integer, the degree
- S, an instance of the type LieSubSpace,
- f, an instance of the type LieAlgebraMap,
Outputs:
- r, a ring element, the trace of the map $f$ acting on $S$ in degree $n$

Description

The subspace $S$ in degree $n$ should be invariant under $f$ (which is tested by the program), and the output gives the trace of $f$ acting on $S$ in degree $n$, which is an element in L#Field.

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

o1 = L

o1 : LieAlgebra

i2 : S=lieSubAlgebra{a,b,c}

o2 = S

o2 : FGLieSubAlgebra

i3 : f=map(L,L,{b,c,a})

o3 = f

o3 : LieAlgebraMap

i4 : trace(3,S,f)

o4 = -1

     ZZ
o4 : --
     31

i5 : f c b a

o5 = (b c a) - (c b a)

o5 : L

i6 : f b c a

o6 =  - (c b a)

o6 : L

Ways to use this method: