A notion of rank for noncommutative quadratic forms on four generators

TL;DR

This paper extends the concept of mu-rank to noncommutative quadratic forms on four generators, building on prior work for fewer generators, and provides definitions for mu-rank one and two in this context.

Contribution

It introduces a new definition of mu-rank for noncommutative quadratic forms on four generators, expanding the theoretical framework.

Findings

Defined mu-rank one and two for four-generator forms

Extended previous mu-rank concepts to higher number of generators

Provides a foundation for further classification of noncommutative quadratic forms

Abstract

In this paper, we extend previous work, where a notion of rank, called mu-rank, was proposed for noncommutative quadratic forms on two and three generators. In particular, we provide a definition of mu-rank one and two for noncommutative quadratic forms on four generators.