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Associative triple trisystems and standard embeddings
Ra\'ul Felipe, Guillermo Vera de Salas
https://arxiv.org/abs/2506.04191 https://

Associative triple trisystems and standard embeddings
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 d…