Nilpotent Symplectic Alternating 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.

125 pages, PhD thesis