Читать книгу Algebra and Applications 2 - Группа авторов - Страница 49

An assosymmetric algebra is a vector space endowed with a bilinear operation that is both left and right pre-Lie, which means that the associator a * (b * c) – (a ∗ b) ∗ c is symmetric under the permutation group S₃. This notion was introduced by Kleinfeld (1957) (see also Hentzel et al. (1996)). All associative algebras are obviously assosymmetric; however, the converse is not true.