Construction of Commutator Blueprints

TL;DR

This paper develops new Weyl-invariant commutator blueprints, expanding the construction of exotic RGD-systems over _2 with specific commutation properties, contributing to the understanding of algebraic structures related to RGD-systems.

Contribution

It introduces several families of Weyl-invariant commutator blueprints, mainly of universal type, and combines these with previous results to produce new exotic RGD-systems over _2.

Findings

Construction of new Weyl-invariant commutator blueprints

Generation of exotic RGD-systems of universal type over _2

Extension of existing frameworks for RGD-system construction

Abstract

Commutator blueprints can be seen as blueprints for constructing RGD-systems over $\mathbb{F}_2$ with prescribed commutation relations. In this paper we construct several families of Weyl-invariant commutator blueprints, mostly of universal type. Together with the main result of \cite{BiRGD} we obtain new examples of exotic RGD-systems of universal type over $\mathbb{F}_2$.