Local decomposition and linearization of Loday brackets

TL;DR

The paper investigates local splitting and linearization techniques for Loday and Courant algebroids, providing new proofs and principles for their structural analysis.

Contribution

It introduces a direct proof of the Courant algebroid splitting theorem and establishes a general linearization principle using Euler-like derivations.

Findings

Provided a new proof of the Courant algebroid splitting theorem

Developed a linearization principle for Loday algebroids

Analyzed local decomposition techniques for Loday brackets

Abstract

We study local splitting-type results for general Loday algebroids and use them to obtain a direct proof of the splitting theorem for Courant algebroids. We also discuss the linearization problem and establish a general linearization principle using Euler-like derivations.