isIsomorphic -- tests whether two Lie algebra modules are isomorphic

Synopsis

Usage:

isIsomorphic(V,W)
Inputs:
- V, an instance of the type LieAlgebraModule,
- W, an instance of the type LieAlgebraModule,
Outputs:
- b, a Boolean value,

Description

To test whether two Lie algebra modules are isomorphic, we first test whether they are modules over the same Lie algebra, and if so, then test whether they have the same decomposition into irreducible Lie algebra modules.

i1 : g=simpleLieAlgebra("A",2)

o1 = g

o1 : LieAlgebra

i2 : M=irreducibleLieAlgebraModule({2,1},g)

o2 = M

o2 : g module

i3 : N=irreducibleLieAlgebraModule({1,2},g)

o3 = N

o3 : g module

i4 : Z=irreducibleLieAlgebraModule({0,0},g)

o4 = Z

o4 : g module

i5 : isIsomorphic(M,N)

o5 = false

i6 : isIsomorphic(M,M)

o6 = true

i7 : isIsomorphic(M,M**Z)

o7 = true

i8 : isIsomorphic(M**N,N**M)

o8 = true

Ways to use `isIsomorphic` :

"isIsomorphic(LieAlgebraModule,LieAlgebraModule)"

For the programmer

The object isIsomorphic is a method function.

isIsomorphic -- tests whether two Lie algebra modules are isomorphic

Synopsis

Description

Ways to use isIsomorphic :

For the programmer

Ways to use `isIsomorphic` :