Associative triple trisystems and standard embeddings
Rings and Algebras
2025-06-05 v1
Abstract
Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any associative triple trisystem.
Cite
@article{arxiv.2506.04191,
title = {Associative triple trisystems and standard embeddings},
author = {Raúl Felipe and Guillermo Vera de Salas},
journal= {arXiv preprint arXiv:2506.04191},
year = {2025}
}