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The actor of a crossed module in Lie algebras. (English) Zbl 0922.17013
Authors’ abstract: In the category $${\mathfrak {CM}}$$ of crossed modules in Lie algebras we introduce the actor of a crossed module, an object that plays a similar role to derivations of a Lie algebra in the category of Lie algebras. From this concept we derive fundamental notions in $${\mathfrak {CM}}$$ such as the centre of a crossed module and the action between crossed modules. Using this concept of action we obtain a description of a crossed square (crossed module in the category of crossed modules).

##### MSC:
 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17B05 Structure theory for Lie algebras and superalgebras 18E99 Categorical algebra
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