Using the knowledge about the finite-dimensional irreducible modules over \(\mathfrak {sl}_2({\mathbb {C}})\), it is possible to associate for any of them an irreducible module 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 \(\mathfrak {sl}_2({\mathbb {C}})\)-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.

利用关于\（\ mathfrak {sl} _2（{\ mathbb {C}}）\）上的有限维不可约模块的知识，可以将它们中的任何一个都归结到四维零维上的不可约模块。交换幂次代数类上的代数。这种关联允许从\（\ mathfrak {sl} _2（{\ mathbb {C}}）\） -类的模块构造到四维零代数模块的类别的嵌入。此外，在本文中，示出了对于任何Ñ大于或等于二，存在尺寸3的不可约模块的两个非同构家庭Ñ超过尺寸四个零乘法的交换功率结合代数。