Cosymplectic Jacobi-Jordan Algebras

TL;DR

This paper introduces cosymplectic structures on Jacobi-Jordan algebras, explores their relation to symplectic counterparts, and provides a classification in dimension five, highlighting their algebraic properties and extension methods.

Contribution

It defines cosymplectic Jacobi-Jordan algebras, studies their properties, and classifies all such algebras in five dimensions for the first time.

Findings

Cosymplectic Jacobi-Jordan algebras support a right-skew-symmetric product.

A complete classification of five-dimensional cosymplectic Jacobi-Jordan algebras is provided.

Double extension constructions are used to analyze these algebras.

Abstract

We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study the double extension constructions of cosymplectic Jacobi-Jordan algebras and give a complete classification in dimension five.