Rota-Baxter type operators on trusses and derived structures
T. Chtioui, M. Elhamdadi, S. Mabrouk, A. Makhlouf
TL;DR
The paper advances operator theory on trusses by defining and exploring Rota-Baxter, Reynolds, Nijenhuis, and averaging operators in the truss setting, and by constructing a family of derived structures such as dendriform trusses, tridendriform trusses, and NS-trusses. It establishes graph- and product-based characterizations that connect RB, Reynolds, and Nijenhuis operators to corresponding split-structure frameworks, and demonstrates categorical correspondences with rings and dendriform rings via subadjacent constructions. The results unify and extend classical operator theory within a general, ternary-based algebraic context, revealing new platforms (di-/tri-trusses, NS-trusses) for decomposing multiplications and distributing laws. These contributions enrich universal algebra and provide tools for translating operator-theoretic insights across rings, braces, and their truss generalizations, with potential applications in related algebraic and combinatorial settings.
Abstract
The aim of this paper is to introduce and study the concepts of the Rota-Baxter operator and Reynolds operator within the framework of trusses. Moreover, we introduce and discuss dendriform trusses, tridendriform trusses, and NS-trusses as fundamental algebraic structures underlying these classes of operators. Furthermore, we consider the notions of Nijenhuis operator and averaging operator to trusses, exploring their properties and applications to uncover new algebraic structures.