# 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:
• Outputs:
• r, , 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