Geodesic
The homology of the lamplighter Lie algebra
Algebra i logika, Tome 60 (2021) no. 6, pp. 636-646
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It is proved that the associated Lie algebra of the Mal'tsev $\mathbb{Q}$-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.
Keywords: homology of Lie algebras, Mal'tsev completion, lamplighter Lie algebra, lamplighter group. 
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Y. Félix; A. Murillo. The homology of the lamplighter Lie algebra. Algebra i logika, Tome 60 (2021) no. 6, pp. 636-646. http://geodesic.mathdoc.fr/item/AL_2021_60_6_a7/

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