Journal of Lie Theory

no. 2
Ideally r-Constrained Graded Lie Subalgebras of Maximal Class Algebras
Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 411-418
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 $r\geq 1$.
DOI: 10.5802/jolt.1389
Classification: 17B70, 17B65, 17B50
Keywords: Ideally r-constrained Lie algebras, Lie algebras of maximal class, just-infinite dimensional Lie algebras, thin algebras, graded Lie algebras 
@article{JOLT_2025_35_2_a7,
     author = {M. Avitabile and N. Gavioli and V. Monti},
     title = {Ideally {r-Constrained} {Graded} {Lie} {Subalgebras} of {Maximal} {Class} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {411--418},
     year = {2025},
     volume = {35},
     number = {2},
     doi = {10.5802/jolt.1389},
     zbl = {08075078},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1389/}
}
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M. Avitabile; N. Gavioli; V. Monti. Ideally r-Constrained Graded Lie Subalgebras of Maximal Class Algebras. Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 411-418. doi: 10.5802/jolt.1389

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