Simple quotient algebras and subalgebras of Jacobian algebras
A Jacobian algebra is an \(n\)-Lie algebra with an \(n\)-ary multiplication operation defined by means of a certain Jacobian. Answering the question posed by \textit{V. T. Filippov} in [Sib. Math. J. 39, No. 3, 573-581 (1998; Zbl 0936.17005)], the author proves that, for certain subalgebras of Jacobian algebras, the quotient algebras by centers are simple. In particular, the first examples are constructed of simple finite-dimensional \(n\)-Lie algebras over a field of characteristic \(p>0\), namely, of dimensions \(p^n-1,\;p^n-2,\;p^{n-1}\), and \(p^{n-1}-1\).
scientific article; zbMATH DE number 1432400
scientific article