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Mat. Zametki, 1976, Volume 19, Issue 6, Pages 833–842 (Mi mz7804)  

Semiplane lattices over irreducible groups

P. Ya. Grushko

Irkutsk State University

Abstract: Among transitive $G$-lattices we can distinguish a rather broad class of so-called semiplane lattices associated with the semidirect product of a Lie group $H$ and a certain automorphism group $G$ of it. It turns out that semiplane lattices are almost always plane in the irreducible case, i.e., we can take it that group $H$ is commutative. An exception is the case of the adjoined representation of a simple Lie group. We have also proved that if group $G$ is involutive and has a “small” radical, then all transitive $G$-lattices turn out to be semiplane.

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English version:
Mathematical Notes, 1976, 19:6, 491–496

Bibliographic databases:

UDC: 513
Received: 10.02.1975

Citation: P. Ya. Grushko, “Semiplane lattices over irreducible groups”, Mat. Zametki, 19:6 (1976), 833–842; Math. Notes, 19:6 (1976), 491–496

Citation in format AMSBIB
\Bibitem{Gru76}
\by P.~Ya.~Grushko
\paper Semiplane lattices over irreducible groups
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 6
\pages 833--842
\mathnet{http://mi.mathnet.ru/mz7804}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=498758}
\zmath{https://zbmath.org/?q=an:0341.53021|0333.53029}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 6
\pages 491--496
\crossref{https://doi.org/10.1007/BF01149924}


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