Embedding of $$\mathfrak {sl}_2({\mathbb {C}})$$-Modules into Four-Dimensional Power-Associative Zero-Algebra Modules

On Albert Problem and Irreducible Modules

“…, 3 n−1 have been constructed by using the method described in ([13], Proposition 1). For n = 4, in [15], families of examples of dimension 3n for any n ≥ 2 were constructed.…”

“…, n − 1 over the zero algebra of dimension n. After that, in [14], the low commutative power-associative nilalgebras and their annihilator were studied. In [15], the author provided families of irreducible modules of dimension 3n for the zero algebra of dimension four, although a complete classification of finite-dimensional irreducible modules for this algebra was not achieved.…”