Journal of Lie Theory 32 (2022), No. 2, 313--326
Copyright Heldermann Verlag 2022
Crossed Extensions of Lie Algebras
Apurba Das
Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India
apurbadas348@gmail.com
[Abstract-pdf]
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 $H^{n+1}_{CE} (\mathfrak{g}, M)$.
Keywords: Lie algebras, Chevalley-Eilenberg cohomology, crossed modules, crossed extensions.
MSC: 17B56, 17B55, 17A32.
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