A Class of Nonassociative Algebras Including Flexible and Alternative Algebras, Operads and Deformations
Remm E* and Goze M
Associate Professor, Université de Haute Alsace, 18 Rue des Frères Lumière, 68093 Mulhouse Cedex, France
- Corresponding Author:
- Remm E
Associate Professor, Université de
Haute Alsace 18 Rue des Frères Lumière
68093 Mulhouse Cedex, France
E-mail: [email protected]
Received date: October 15, 2015; Accepted date: November 10, 2015; Published date: November 17, 2015
Citation: Remm E, Goze M (2015) A Class of Nonassociative Algebras Including Flexible and Alternative Algebras, Operads and Deformations. J Generalized Lie Theory Appl 9:235. doi:10.4172/1736-4337.1000235
Copyright: © 2015 Remm E, 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.
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group Σ3. The first one corresponds to the Lie-admissible algebras and this class has been studied in a previous paper of Remm and Goze. Here we are interested by the second one corresponding to the third power associative algebras.