From n-systems to Lie and Courant algebroids

TL;DR

This paper presents a new method for constructing various types of algebroids, including Lie and Courant algebroids, using the concept of n-systems on vector bundles, with explicit computations of structure maps.

Contribution

It introduces the concept of n-systems and metric n-systems for constructing and explicitly computing structure maps of algebroids, expanding the toolkit for algebroid theory.

Findings

Explicit construction of structure maps for algebroids from n-systems

Introduction of metric n-systems for metric algebroids

Framework applicable to a broad class of algebroids

Abstract

This paper introduces a method for constructing pure algebroids, dull algebroids, and Lie algebroids. The construction relies on what we deffned as n-systems on vector bundles, and we provide explicit computations for all resulting structure maps. Analogously, metric n-systems deffned on metric vector bundles allow us to construct metric algebroids, pre-Courant algebroids, and Courant algebroids.