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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 4

Actor of a crossed module of dialgebras via tetramultipliers

José Manuel Casas(Universidade de Vigo)0000-0002-6556-6131
Rafael Fernandez-casado(Universidade de Santiago de Compostela)0000-0003-1347-6879
Xabier Garcia Martinez(Universidade de Vigo)0000-0003-1679-4047
Emzar Khmaladze(Tbilisi State University)0000-0001-9492-982X
Pages
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Publication Date
2021-08-06
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AI Summary & Key Takeaways

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⚡ 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).
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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., Fernandez-casado, R., Martinez, X. G., Khmaladze, E. (2021). Actor of a crossed module of dialgebras via tetramultipliers. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 4. https://doi.org/10.15672/hujms.701217

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