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.