Algebra, Hyperalgebra and Lie-Santilli Theory
- Corresponding Author:
- Davvaz B
Department of Mathematics
Yazd University, Yazd, Iran
E-mail: [email protected]
Received date: August 06, 2014; Accepted date: October 13, 2015; Published date: October 19, 2015
Citation: Davvaza B, Santilli RM, Vougiouklis T (2015) Algebra, Hyperalgebra and Lie-Santilli Theory. J Generalized Lie Theory Appl 9:231. doi:10.4172/1736-4337.1000231
Copyright: © 2015 Davvaza B, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.