On minimal symplectic alternating algebras

Abstract

The structure of nilpotent symplectic algebras of maximal class has been studied in [8, 5]. In this paper, we study the dual subclass of algebras of minimal class. In particular, we show that symplectic alternating algebras of dimension up to $16$ that are minimal, in the sense that they are of rank $2$ with minimum nilpotency class, have a class that confirm a conjecture that has been raised in [3].