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arXiv · 2506.04191

Associative triple trisystems and standard embeddings

Raúl Felipe·Guillermo Vera de Salas
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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.

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Raúl Felipe, Guillermo Vera de Salas. 2025-06-04. Associative triple trisystems and standard embeddings. https://arxiv.org/abs/2506.04191

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