Crossed modules of ternary Leibniz algebras
Kol B\'eatrice Gamou, Ibrahima Bakayoko
TL;DR
This paper develops new algebraic structures called crossed modules for ternary Leibniz algebras, linking them to related algebraic systems like Leibniz and triassociative algebras.
Contribution
It introduces constructions of triassociative algebras and crossed modules from existing structures, establishing connections between different algebraic frameworks.
Findings
Constructed triassociative algebras from operators
Defined new actions and crossed modules for ternary Leibniz algebras
Established links between Leibniz, triassociative, and ternary Leibniz algebras
Abstract
The aim of this paper is to construct triassociative algebras (from operators), new actions and crossed modules from a given one, and to make the connexion between these notions on Leibniz algebras or triassociative algebras and the corresponding notions on ternary Leibniz algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras