Nilpotent Symplectic Alternating Algebras

TL;DR

This paper develops a structure theory for nilpotent symplectic alternating algebras and classifies all such algebras up to dimension 10, introducing new subclasses of groups.

Contribution

It provides a classification of nilpotent symplectic alternating algebras up to dimension 10 and introduces the concepts of powerfully nilpotent and powerfully soluble groups.

Findings

Classification of all nilpotent symplectic alternating algebras up to dimension 10

Introduction of powerfully nilpotent and powerfully soluble groups

Development of a new structure theory for these algebras

Abstract

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful groups that we call powerfully nilpotent groups and powerfully soluble groups.