The actor of a crossed module in Lie algebras. (English) Zbl 0922.17013

Casas, J. M.; Ladra, M.

Commun. Algebra 26, No. 7, 2065-2089 (1998).

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

Keywords:

category of crossed modules; derivations; Lie algebras; crossed square

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