Bekzat Zhakhayev ; Askar Dzhumadil'daev ; Saule Abdykassymova - Assosymmetric Operad

cm:9740 - Communications in Mathematics, September 19, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9740
Assosymmetric OperadArticle

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

    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.


    Volume: Volume 30 (2022), Issue 1
    Published on: September 19, 2022
    Accepted on: June 24, 2021
    Submitted on: June 25, 2022
    Keywords: Free assosymmetric algebras, Specht module, Weyl module, cocharacter, codimension, colength.

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