Actor of a crossed module of dialgebras via tetramultipliers

Year 2021, Volume: 50 Issue: 4, 1063 - 1078, 06.08.2021

José Manuel Casas Rafael Fernandez-casado , Xabier Garcia Martinez , Emzar Khmaladze

https://doi.org/10.15672/hujms.701217

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 (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

Supporting Institution

Ministerio de Economía y Competitividad

Project Number

MTM2016-79661-P

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