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.

UDC: 513

Received: 10.02.1975

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

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