Geodesic
Actor of a crossed module of Leibniz algebras
Theory and applications of categories, Tome 33 (2018), pp. 23-42

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We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra. This results into a pair of Leibniz algebras which allow us to construct an object which is the actor under certain circumstances. Additionally, we give a description of an action in the category of crossed modules of Leibniz algebras in terms of equations. Finally, we check that, under the aforementioned conditions, the kernel of the canonical map from a crossed module to its actor coincides with the center and we introduce the notions of crossed module of inner and outer biderivations.

Publié le :
Classification : 17A30, 17A32, 18A05, 18D05
Keywords: Leibniz algebra, crossed module, representation, actor 
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     author = {Jos\'e Manuel Casas and Rafael Fern\'andez-Casado and Xabier Garc{\'\i}a-Mart{\'\i}nez and Emzar Khmaladze},
     title = {Actor of a crossed module of {Leibniz} algebras},
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     volume = {33},
     year = {2018},
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José Manuel Casas; Rafael Fernández-Casado; Xabier García-Martínez; Emzar Khmaladze. Actor of a crossed module of Leibniz algebras. Theory and applications of categories, Tome 33 (2018), pp. 23-42. http://geodesic.mathdoc.fr/item/TAC_2018_33_a1/