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

Abstract

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

The authors thank Chengming Bai for guidance and important discussion. All authors are supported by Innovation and Entrepreneurship Training Program for College Students of Tianjin 202010055305

References in corpus (1)

• A complete classification of three-dimensional algebras over $\mathbb{R}$ and $\mathbb{C}$