Assosymmetric Operad

descriptionPublicationkeyboard_double_arrow_right Article 19 Sep 2022 English Publisher:Centre pour la Communication Scientifique Directe (CCSD)Journal:Communications in Mathematics, volume Volume 30 (2022), Issue 1 (eissn: 2336-1298,

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

doi: 10.46298/cm.9740 , 10.5281/zenodo.6991800 , 10.5281/zenodo.6735104 , 10.5281/zenodo.6735105

Assosymmetric Operad

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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.

Related Organizations

Suleyman Demirel University
Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakhstan

Keywords

Weyl module, Nonassociative algebras satisfying other identities, Specht module, Free assosymmetric algebras, Specht module, Weyl module, cocharacter, codimension, colength., Representations of finite symmetric groups, codimension, colength, Free nonassociative algebras, free assosymmetric algebras, cocharacter

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