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.

21 pages; in v3 we added more references, we improved the presentation and added few more examples. Final version, accepted for publication in J. Pure Appl. Algebra