Generalized NS-algebras

TL;DR

This paper extends the concept of NS-algebras to arbitrary algebraic categories using bimodule properties, connecting various operators like Nijenhuis and Rota-Baxter to these generalized structures.

Contribution

It introduces a unified framework for NS-algebras across categories, incorporating multiple operator types such as Nijenhuis and Rota-Baxter operators.

Findings

Generalized NS-algebras to arbitrary categories.

Established connections with Nijenhuis, twisted Rota-Baxter, and relative Rota-Baxter operators.

Unified approach broadening the applicability of NS-algebras.

Abstract

We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of operators lead to NS-algebras: Nijenhuis operators, twisted Rota-Baxter operators and relative Rota-Baxter operators of arbitrary weight.