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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 31–40 (Mi mz7622)  

This article is cited in 3 scientific papers (total in 4 papers)

Semidirect sums of Lie algebras

A. L. Onishchik, Yu. B. Khakimdzhanov

M. V. Lomonosov Moscow State University

Abstract: This paper examines the problem of classifying finite-dimensional Lie algebras over the field $C$ with a given radical $\mathfrak{r}$ and also the problem of classifying algebraic Lie algebras with a given nilpotent radical $\mathfrak{r}$. A detailed study is made of the case when $\mathfrak{r}$ is the nilpotent radical of a parabolic subalgebra of a semisimple Lie algebra.

Full text: PDF file (835 kB)

English version:
Mathematical Notes, 1975, 18:1, 600–604

Bibliographic databases:

UDC: 519.46
Received: 16.04.1974

Citation: A. L. Onishchik, Yu. B. Khakimdzhanov, “Semidirect sums of Lie algebras”, Mat. Zametki, 18:1 (1975), 31–40; Math. Notes, 18:1 (1975), 600–604

Citation in format AMSBIB
\Bibitem{OniKha75}
\by A.~L.~Onishchik, Yu.~B.~Khakimdzhanov
\paper Semidirect sums of Lie algebras
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 31--40
\mathnet{http://mi.mathnet.ru/mz7622}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=427409}
\zmath{https://zbmath.org/?q=an:0322.17003}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 600--604
\crossref{https://doi.org/10.1007/BF01461138}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. B. Khakimdzhanov, “On the cohomology of some nilpotent Lie algebras”, Math. USSR-Sb., 67:1 (1990), 99–116  mathnet  crossref  mathscinet  zmath  isi
    2. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, V. G. Durnev, R. Zulanke, L. S. Kazarin, D. A. Leites, V. V. Serganova, V. M. Tikhomirov, “Arkadii L'vovich Onishchik (on his 70th birthday)”, Russian Math. Surveys, 58:6 (2003), 1245–1253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Gorbatsevich, “On algebraic Anosov diffeomorphisms on nilmanifolds”, Siberian Math. J., 45:5 (2004), 821–839  mathnet  crossref  mathscinet  zmath  isi
    4. V. V. Gorbatsevich, “On the maximal finite-dimensional Lie algebras with given nilradical”, Russian Math. (Iz. VUZ), 59:2 (2015), 29–35  mathnet  crossref
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