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

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

See also

• isIsomorphism(LieAlgebraMap) -- whether a Lie map is an isomorphism
• isWellDefined(ZZ,LieAlgebraMap) -- whether a Lie map is well defined