The theory of hyperstructures can offer to the Lie-Santilli Theory a variety of models to specify the mathematical representation of the related theory. In this paper we focus on the appropriate general hyperstructures, especially on hyperstructures with hyperunits. We define a Lie hyperalgebra over a hyperfield as well as a Jordan hyperalgebra, and we obtain some results in this respect. Finally, by using the concept of fundamental relations we connect hyper algebras to Lie algebras and Lie-Santilli-addmissible algebras.
"Algebra, Hyperalgebra and Lie-Santilli Theory." J. Gen. Lie Theory Appl. 9 (2) 1 - 5, 2015. https://doi.org/10.4172/1736-4337.1000231