Classification of pre-Jordan Algebras and Rota-Baxter Operators on Jordan Algebras in Low Dimensions

TL;DR

This paper classifies low-dimensional complex pre-Jordan algebras and Rota-Baxter operators on Jordan algebras, providing a comprehensive understanding of their structures and interrelations in dimensions up to three.

Contribution

It offers the first complete classification of complex pre-Jordan algebras and Rota-Baxter operators in low dimensions, expanding the structural theory of Jordan-related algebras.

Findings

Complete classification of complex pre-Jordan algebras in dimensions ≤ 3

Explicit description of Rota-Baxter operators on Jordan algebras in dimensions ≤ 3

Identification of induced pre-Jordan algebra structures

Abstract

This paper is devoted to the classification of complex pre-Jordan algebras in the sense of isomorphisms in dimensions $\leq$ 3. All Rota-Baxter operators on complex Jordan algebras in dimensions $\leq$ 3 and the induced pre-Jordan algebras are also presented.