Embedding of sl(2)(C)-Modules into Four-Dimensional Power-Associative Zero-Algebra Modules

Using the knowledge about the finite-dimensional irreducible modules over sl(2)(C), it is possible to associate for any of them an irreduciblemodule over the four-dimensional zero-algebra on the class of commutative power-associative algebras. This association allows to construct an embedding from the category of sl(2)(C)-modules into the category of the four-dimensional zero-algebra modules. Furthermore, in this paper it is shown that for any n greater than or equal to two, there exist two non-isomorphic families of irreducible modules of dimension 3n over the commutative power-associative algebra of dimension four and zero multiplication.