*WINNER* mu-rank of Noncommutative Quadratic Forms on Four Generators

Abstract

In 2010, Cassidy and Vancliff extended the notion of commutative quadratic forms to the noncommutative setting. This led to a definition of a notion of a rank, referred to as mu-rank, for quadratic forms on two and three generators. For quadratic forms on four generators, a definition for mu-rank was developed by Frauendienst and Veerapen. In this project, we examine this further. We take our field to be algebraically closed with characteristic not equal to two.