Dendriform algebras and Rota-baxter operators revisited in several directions
The main purpose of this article is to move the study of dendriform algebras and Rota-Baxter operators to a nonassociative setting beyond the Lie algebras. We show how to associate structures of dendriform type to alternative and exible algebras and characterize the Rota-Baxter op- erators correspon...
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| Tipo de recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| Idioma: | inglés |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/590 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/590 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/MSC/Algebras Dendriform info:eu-repo/classification/MSC/Algebras de Leibniz info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1201 info:eu-repo/classification/cti/120199 |
| Sumario: | The main purpose of this article is to move the study of dendriform algebras and Rota-Baxter operators to a nonassociative setting beyond the Lie algebras. We show how to associate structures of dendriform type to alternative and exible algebras and characterize the Rota-Baxter op- erators corresponding to them, in order to extend some results that have appeared in the literature for the associative case. These objects are stud- ied in some detail. Also, we show that the usual version of Rota-Baxter operators acts on Leibniz algebras in the same form that they act on Lie algebras and in particular can be used into Leibniz-admissible algebras. As a consequence we arrive to the notion of admissible dendriform al- gebra. Additionally, we propose the concept of generalized dendriform algebra and describe a connection of it with the left-symmetric dialgebras recently introduced by the author. |
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