3-nil alternative, pre-Lie and assosymmetric operads
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Date
2026
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
SDU University
Abstract
An algebra is called alternative if it satisfies the following identities: (ab)c − a(bc) = −(ac)b + a(cb), (ab)c − a(bc) = −(ba)c + b(ac). In this dissertation, we consider free alternative algebra with the additional identity x 3 = 0. For motivation, we refer to the dual operad of the alternative operad. Also, we obtain pre-Lie algebra with the identity x 3 = 0 from binary perm algebra. Finally, we consider assosymmetric algebra with identity x 3 = 0
Description
Keywords
Anti-Leibniz algebras, The variety of alternative algebras, Koszul dual operad
Citation
Tekebay A / 3-nil alternative, pre-Lie and assosymmetric operads / SDU University / Department of Mathematics and Natural Sciences