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Journal of Lie Theory 35 (2025), No. 2, 411--418 Copyright Heldermann Verlag 2025 Ideally r-Constrained Graded Lie Subalgebras of Maximal Class Algebras Marina Avitabile Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Milano, Italy marina.avitabile@unimib.it Norberto Gavioli Dip. di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi dell'Aquila, Coppito, Italy norberto.gavioli@univaq.it Valerio Monti Dip. di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, Como, Italy valerio.monti@uninsubria.it [Abstract-pdf] Let $E\supseteq F$ be a field extension and $M$ a graded Lie algebra of maximal class over $E$. We investigate the $F$-subalgebras $L$ of $M$, generated by elements of degree $1$. We provide conditions for $L$ being either ideally $r$-constrained or not just infinite. We show by an example that those conditions are tight. Furthermore, we determine the structure of $L$ when the field extension $E\supseteq F$ is finite. A class of ideally $r$-constrained Lie algebras which are not $(r-1)$-constrained is explicitly constructed, for every $r\geq 1$. Keywords: Ideally r-constrained Lie algebras, Lie algebras of maximal class, just-infinite dimensional Lie algebras, thin algebras, graded Lie algebras. MSC: 17B70; 17B65, 17B50. [ Fulltext-pdf (114 KB)] open access. |