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# LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules

- Operator: **
- Usage:
    `U ** V`
- Inputs:
  - U, an instance of the type LieAlgebraModule,
  - V, an instance of the type LieAlgebraModule,
- Outputs:
  - W, an instance of the type LieAlgebraModule,

## Description

Computes the tensor product of two Lie algebra modules.

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

    o1 = g

    o1 : simple LieAlgebra

    i2 : U=irreducibleLieAlgebraModule({4,2},g)

    o2 = U

    o2 : irreducible LieAlgebraModule over g

    i3 : V=irreducibleLieAlgebraModule({3,1},g)

    o3 = V

    o3 : irreducible LieAlgebraModule over g

    i4 : U**V

                                                                   2              2                                      2              2                          2
    o4 = LL   (g) ++ LL   (g) ++ LL   (g) ++ LL   (g) ++ (LL   (g))  ++ (LL   (g))  ++ LL   (g) ++ LL   (g) ++ (LL   (g))  ++ (LL   (g))  ++ LL   (g) ++ (LL   (g))  ++ LL   (g) ++ LL   (g) ++ LL   (g)
           0,5         1,3         1,6         2,1          2,4            3,2           3,5         4,0          4,3            5,1           5,4          6,2           7,0         7,3         8,1

    o4 : LieAlgebraModule over g

## See also

- tensorCoefficient -- computes the multiplicity of W in U tensor V

## Ways to use this method:

- LieAlgebraModule ** LieAlgebraModule -- tensor product of LieAlgebraModules

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:823:0.