Journal of Lie Theory

no. 2
Crossed Extensions of Lie Algebras
Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 313-326
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 $H^{n+1}_{CE} (\mathfrak{g}, M)$.
DOI: 10.5802/jolt.1233
Classification: 17B56, 17B55, 17A32
Keywords: Lie algebras, Chevalley-Eilenberg cohomology, crossed modules, crossed extensions 
@article{JOLT_2022_32_2_a1,
     author = {A. Das},
     title = {Crossed {Extensions} of {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {313--326},
     year = {2022},
     volume = {32},
     number = {2},
     doi = {10.5802/jolt.1233},
     zbl = {1486.17032},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1233/}
}
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A. Das. Crossed Extensions of Lie Algebras. Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 313-326. doi: 10.5802/jolt.1233

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