Some Results on Zinbiel Algebras and Rota–Baxter Operators

Abstract

Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally, ZAs are also realized in low dimensions of the RBOs of commutative associative algebras. It was found that not all ZAs can be attained in this way.

Keywords

• Zinbiel algebra
• commutative associative algebra
• Rota–Baxter operator
• deviation