Taoufik Chtioui, Sami Mabrouk, Abdenacer Makhlouf: BiHom-pre-alternative algebras and BiHom-alternative quadri-algebras, 3-21

Abstract:

The purpose of this paper is to introduce and study the notion of BiHom-pre-alternative algebra which may be viewed as a BiHom-alternative algebra whose product can be decomposed into two compatible pieces. Furthermore, we introduce the notion of BiHom-alternative quadri-algebra and show the connections between all these algebraic structures using Rota-Baxter operators and $\mathcal{O}$-operators.

Key Words: BiHom-alternative algebra, BiHom-pre-alternative algebra, BiHom-alternative quadri-algebra, bimodule, $\mathcal{O}$-operator.

2010 Mathematics Subject Classification: Primary 17A30, 17D05;
Secondary 17A36.