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.

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