On Power-Associative Nilalgebras of Dimension N and Nilindex N-1

Abstract

Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n − 1 based on the condition that n − 4 ≤ dim 𝔄3 ≤ n − 3. This paper is a continuation of [10], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2].