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This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
Questa Nota vuole provare che in certi casi, data un'algebra di Lie , esistono due gruppi di Lie, G e H, con algebra di Lie tali che G ha, ma H non ha mai, una rappresentazione lineare fedele.
Questa Nota presenta un criterio tale che un'algebra di Lie reale o complessa di dimensione finita sia nilpotente nei termini dei valori caratteristici di un automorfismo e fornisce una maggiorazione degli indici n di nilpotenza. Infatti questa maggiorazione è la migliore possibile. Nel caso n = 2 si dimostra anche l'inverso e se ne deduce che un gruppo di Lie connesso e semplicemente connesso con n = 2 ha sempre una famiglia moltiplicativa degli automorfismi tale che per ogni .
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