TY - JOUR
T1 - Actor of a crossed module of dialgebras via tetramultipliers
AU - Garcia Martinez, Xabier
AU - Casas, José Manuel
AU - Fernandez-casado, Rafael
AU - Khmaladze, Emzar
PY - 2021
DA - August
DO - 10.15672/hujms.701217
JF - Hacettepe Journal of Mathematics and Statistics
PB - Hacettepe Üniversitesi
WT - DergiPark
SN - 2651-477X
SP - 1063
EP - 1078
VL - 50
IS - 4
LA - en
AB - 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.
KW - Dialgebra
KW - crossed module
KW - tetramultiplier
KW - representation
KW - actor
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UR - https://doi.org/10.15672/hujms.701217
L1 - https://dergipark.org.tr/tr/download/article-file/999589
ER -