Constructing towers with skeletons from open Lie algebras and integrability

TL;DR

This paper introduces a method to construct towers using open Lie algebra skeletons, linking algebraic structures to integrability conditions through dispersive nonlinear models and conservation laws.

Contribution

It presents a novel approach to associate algebraic skeletons with integrability conditions, connecting Lie algebra structures to nonlinear dispersive models.

Findings

Identifies conditions for integrability via algebraic skeletons.

Links conservation laws to spectral problems.

Provides a framework for constructing integrable models.

Abstract

We provide a given algebraic structure with the structure of an infinitesimal algebraic skeleton. The necessary conditions for integrability of the absolute parallelism of a tower with such a skeleton are dispersive nonlinear models and related conservation laws given in the form of associated linear spectral problems.