zbMATH — the first resource for mathematics

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).

17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B05 Structure theory for Lie algebras and superalgebras
18E99 Categorical algebra
Full Text: DOI
[1] Casas J.M., Ph. D. Thesis (1990)
[2] Chow Y., General theory of Lie algebras (1978) · Zbl 0384.17004
[3] Ellis G.J., Ph. D. Thesis (1984)
[4] Ellis G.J., I.M.S. Bulletin 21 pp 29– (1988)
[5] Gordon R., Cahiers de Topologie et Géométrie Différentielle Catégoriques 4 pp 305– (1993)
[6] Guin D., Ann. Inst. Fourier 45 pp 93– (1995) · Zbl 0818.17022
[7] DOI: 10.1093/qmath/19.1.363 · Zbl 0165.03301
[8] Jacobson N., Lie algebras (1962)
[9] DOI: 10.5802/aif.896 · Zbl 0485.17006
[10] DOI: 10.1112/blms/11.1.8 · Zbl 0416.20030
[11] Mitchell B., Theory of categories (1965) · Zbl 0136.00604
[12] Norrie K.J., Ph. D. Thesis (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.