Actor of a crossed module of dialgebras via tetramultipliers

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Hacettepe Journal of Mathematics and Statistics
Volume:50 Issue:4
Actor of a crossed module of dialgebras via tetramultipliers

Actor of a crossed module of dialgebras via tetramultipliers

Authors : José Manuel CASAS, Rafael FERNANDEZCASADO, Xabier GARCİA MARTİNEZ, Emzar KHMALADZE

Pages : 1063-1078

Doi:10.15672/hujms.701217

View : 19 | Download : 12

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :We study the representability of actions in the category of crossed modules of dialgebras via tetramultipliers. We deduce a pair of dialgebras in order to construct an object which, under certain circumstances, is the actor insert ignore into journalissuearticles values(also known as the split extension classifier);. Moreover, we give give a full description of actions in terms of equations. Finally, we check that under the aforementioned circumstances, the center coincides with the kernel of the canonical map from a crossed module to its actor.
Keywords : Dialgebra, crossed module, tetramultiplier, representation, actor

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