Authors: Zhakhayev, Bekzat ¹; Dzhumadil'daev, Askar ²; Abdykassymova, Saule ²

• 1 Suleyman Demirel University, Kaskelen, Kazakhstan
• 2 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

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.

• 17A30 - Nonassociative algebras satisfying other identities
• 17A50 - Free nonassociative algebras
• 20C30 - Representations of finite symmetric groups