System of roots

TL;DR

This paper introduces a root system analogue for fundamental sandwich algebras, extending concepts from semisimple Lie algebras and paving the way for defining a corresponding Weyl group.

Contribution

It establishes a new root system framework for fundamental sandwich algebras, generalizing classical Lie algebra structures.

Findings

Fundamental sandwich algebras possess a root system analogue.

An analogue of the Weyl group is constructed for these algebras.

The work sets the stage for further study of symmetry groups in this context.

Abstract

We show that a fundamental sandwich algebra has an analogue of a root system of a semisimple Lie algebra. This leads to an analogue of a Weyl group, which we study in another paper.