Assosymmetric Operad

Abstract

An algebra with identities (a, b, c) = (a, c, b) = (b, a, c) is called assosymmetric, where (x, y, z) = x(yz) − (xy)z is associator. We establish that operad of assosymmetric algebras is not Koszul. We study Sn-module, An-module and GLn-module structures on multilinear parts of assosymmetric operad.

On the free metabelian Novikov and metabelian Lie-admissible algebras

“…The generators of symmetric polynomials in free metabelian Leibniz algebras were found in [24]. Other examples of Lie-admissible algebras are assosymmetric algebras [11]. A basis of the free metabelian Malcev algebra is constructed in [20].…”