BiHom-NS-algebras, twisted Rota-Baxter operators and generalized Nijenhuis operators

TL;DR

This paper introduces BiHom-NS-algebras, explores their connection with twisted Rota-Baxter operators, and generalizes Nijenhuis operators within a BiHom-associative framework, expanding algebraic structures and operator theory.

Contribution

It presents the first comprehensive study of BiHom-NS-algebras, linking them to twisted Rota-Baxter operators and generalizing Nijenhuis operators in a BiHom context.

Findings

BiHom-NS-algebras generalize NS-algebras using two homomorphisms.

Established relationships between BiHom-NS-algebras and twisted Rota-Baxter operators.

Generalized Nijenhuis operators lead to the construction of BiHom-NS-algebras.

Abstract

The purpose of this paper is to introduce and study BiHom-NS-algebras, which are a generalization of NS-algebras using two homomorphisms. Moreover, we discuss their relationships with twisted Rota-Baxter operators in a BiHom-associative context. Furthermore, we introduce a generalization of Nijenhuis operators that lead to BiHom-NS-algebras along BiHom-associative algebras