Geodesic
Crossed Extensions of Lie Algebras
Apurba Das1
1Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India
Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 313-326

Voir la notice de l'article provenant de la source Heldermann Verlag

It is known that Hochschild cohomology groups are represented by crossed extensions of associative algebras. In this paper, we introduce crossed $n$-fold extensions of a Lie algebra $\mathfrak{g}$ by a module $M$, for $n \geq 2$. We show that such extensions represent elements in the $(n+1)$-th Chevalley-Eilenberg cohomology group $H^{n+1}_{CE} (\mathfrak{g}, M)$.
Classification : 17B56, 17B55, 17A32
Mots-clés : Lie algebras, Chevalley-Eilenberg cohomology, crossed modules, crossed extensions

Apurba Das  1

1 Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India 
Apurba Das. Crossed Extensions of Lie Algebras. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 313-326. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a1/
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     title = {Crossed {Extensions} of {Lie} {Algebras}},
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     year = {2022},
     volume = {32},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a1/}
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