Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generalized NS-algebras

Cyrille Ospel, Florin Panaite, Pol Vanhaecke

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.

Generalized 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.

Paper Structure

This paper contains 3 sections, 1 theorem, 14 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. NS-algebras

Key Result

Proposition 2.2

Let $(A,\mu)\in \mathcal{C}$ and let $(M,\bullet)$ be an $A$-bimodule algebra. Then $M$ is an $A$-bimodule.

Theorems & Definitions (6)

  • Definition 1.1
  • Definition 1.2
  • Example 2.1
  • Proposition 2.2
  • proof
  • Definition 3.1