New Lie tori from Naoi tori

TL;DR

This paper introduces a broad class of Lie tori called general Lie tori, demonstrates their relation to Naoi tori, and shows they are isotopic to original Lie tori, providing new ways to define Lie tori from root systems.

Contribution

It generalizes Lie tori, establishes their connection to Naoi tori, and introduces the concept of Lie R-tori for locally extended affine root systems.

Findings

Naoi tori are a special case of general Lie tori

General Lie tori are isotopic to original Lie tori

A simple definition of Lie tori from root systems is proposed

Abstract

We define general Lie tori which generalize original Lie tori. We show that a Naoi torus is a general Lie torus. We give examples and prove several properties of general Lie tori. We also review isotopies of Lie tori, and prove that a general Lie torus is, in fact, isotopic to an original Lie torus. Finally, we suggest a very simple way of defining a Lie torus corresponding to a locally extended affine root system R, which we call a Lie R-torus.