Geodesic
On cohomologies and representations of groups with normal Engel subgroups
Eurasian mathematical journal, Tome 13 (2022) no. 2, pp. 70-81.

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Let $\lambda$, $U$ be representations of a group $G$ with a normal Engel subgroup $N$. The paper studies triviality conditions for the cohomology group $\mathcal{H}^1(G,\lambda,U)$ when $\lambda$ and $U$ are sectionally spectrally disjoint and examines some decompositions of the extension $\mathfrak{e}(\lambda, U,\xi)$ of $\lambda$ by $U$ associated with non-trivial $(\lambda, U)$-cocycles $\xi$. 
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     title = {On cohomologies and representations of groups with normal {Engel} subgroups},
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E. Kissin; V. S. Shulman. On cohomologies and representations of groups with normal Engel subgroups. Eurasian mathematical journal, Tome 13 (2022) no. 2, pp. 70-81. http://geodesic.mathdoc.fr/item/EMJ_2022_13_2_a6/

[1] P. Delorme, “1-cohomologie des representations unitaires des groupes de Lie semisimples et resolubles”, Bull. Soc. Math. France, 105 (1977), 281–336 | DOI | MR | Zbl

[2] A. Guichardet, “Sur la cohomologie des groupes topologiques, II”, Bull. Soc. Math., 96 (1972), 305–332 | MR | Zbl

[3] A. Guichardet, “Cohomology of topological groups and positive definite functions”, J. Multivariate Anal., 3 (1973), 249–261 | DOI | MR | Zbl

[4] A. Guichardet, Cohomologie des groupes topologiques et des algebres de Lie, Cedic/Fernand Nathan, Paris, 1980 | MR | Zbl

[5] P. R. Halmos, A Hilbert space problem book, D. van Nostrand Co. Inc., Princeton–Toronto–London, 1967 | MR | Zbl

[6] E. Kissin, V. S. Shulman, “Non-unitary representations of nilpotent groups, I: cohomologies, extensions and neutral cocycles”, J. Func. Anal., 269 (2015), 2564–2610 | DOI | MR | Zbl

[7] E. Kissin, V. S. Shulman, “Cohomology of groups with normal Engel subgroups”, Proceedings of 10th International Science and Technology Conference, INFOS-2019 (Vologda, 2019), 4–8 | DOI

[8] K. Kuratowski, Topology, v. 1-2, Acad. Press, London, 1966–1968 | Zbl

[9] R. Radjavi, P. Rosenthal, Invariant subspaces, Springer-Verlag, Berlin, 1973 | MR | Zbl