A class of nonassociative algebras including flexible and alternative algebras, operads and deformations. (English) Zbl 1395.17002

Remm, E.; Goze, M.

J. Gen. Lie Theory Appl. 9, No. 2, Article ID 1000235, 6 p. (2015).

Summary: 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 \(\Sigma_3\). The first one corresponds to the Lie-admissible algebras and this class has been studied in a previous paper of the authors [J. Algebra 273, No. 1, 129–152 (2004; Zbl 1045.17007)]. Here we are interested by the second one corresponding to the third power associative algebras.

MSC:

17A30

Nonassociative algebras satisfying other identities

Keywords:

nonassociative algebras; alternative algebras; third power associative algebras; operads

Citations:

Zbl 1045.17007