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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

Actor of a crossed module of dialgebras via tetramultipliers

José Manuel Casas
R. Fernández-Casado
Xabier García Martínez
Emzar Khmaladze
Pages
1063–1078
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study the representability of actions in the category of crossed modules of dialgebras via tetramultipliers.
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Key Findings & Data: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).
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dialgebra · crossed module · tetramultiplier

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.

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Cite This Article

Casas, J. M., Fernández-Casado, R., Martínez, X. G., Khmaladze, E. (2022). Actor of a crossed module of dialgebras via tetramultipliers. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1063–1078. https://ajindex.com/articles/529446

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