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LieTypes :: isIsomorphic

isIsomorphic -- tests whether two Lie algebra modules are isomorphic

Synopsis

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 :