Para-associative Algebroids

TL;DR

This paper introduces para-associative algebroids, a new class of vector bundles with sections forming a ternary algebra, and characterizes their local triviality via the existence of a compatible differential connection.

Contribution

It defines para-associative algebroids and establishes a necessary and sufficient condition for their local triviality based on differential connections.

Findings

Para-associative algebroids are characterized by a ternary algebra structure.

Local triviality is equivalent to the existence of a compatible differential connection.

The work generalizes associative algebroids to a ternary setting.

Abstract

We introduce para-associative algebroids as vector bundles whose sections form a ternary algebra with a generalised form of associativity. We show that a necessary and sufficient condition for local triviality is the existence of a differential connection, i.e., a connection that satisfies the Leibniz rule over the ternary product.