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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/665| Quasi-Jordan Algebras | |
| LAZARO RAUL FELIPE PARADA | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Algebras de Jordan | |
| In this paper we introduce a new algebraic structure of a Jordan type and we show several examples. This new structure called quasi-Jordan algebras appear in the study of the product, where x, y are elements in a dialgrebra ( D, a , ` ). The quasi-Jordan alge- bras are a generalization of the Jordan algebras for which the commutative law is changed by a quasi-commutative identity and a special form of the Jordan identity is retained. The quasi-Jordan algebras are not contained in the generalizations of Jordan algebras, in particular with respect to noncommutative Jordan algebras. We show a few results about the re- lationship between Jordan algebras and quasi-Jordan algebras. Also, we compare quasi-Jordan algebras with some structures. In particular, we found a special relation with the Leibniz algebras. We attach a quasi- Jordan algebra L x to any ad-nilpotent element x with an index of nilpo- tence at most 3 in a Leibniz algebra L . In this part we extended the results of Kostrikin and Benkart-Isaacs about nilpotent elements to Leibniz alge- bras and we show that L x is nondegenerated if L is nondegenerated | |
| Centro de Investigación en Matemáticas AC | |
| 28-09-2006 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| ÁLGEBRAS NO ASOCIATIVAS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Matemáticas |
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