Email this article Maximal Lie subalgebras among locally nilpotent derivations
- Authors: Skutin A.A.1
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: Vol 212, No 2 (2021)
- Pages: 138-146
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/142366
- DOI: https://doi.org/10.4213/sm9360
- ID: 142366
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Abstract
We study maximal Lie subalgebras among locally nilpotent derivations of the polynomial algebra. Freudenburg conjectured that the triangular Lie algebra of locally nilpotent derivations of the polynomial algebra is a maximal Lie algebra contained in the set of locally nilpotent derivations, and that every maximal Lie algebra contained in the set of locally nilpotent derivations is conjugate to the triangular Lie algebra. In this paper we prove the first part of the conjecture and present a counterexample to the second part. We also show that under a certain natural condition imposed on a maximal Lie algebra there is a conjugation taking this Lie algebra to the triangular Lie algebra. Bibliography: 2 titles.
About the authors
Alexander Andreevich Skutin
Lomonosov Moscow State University, Faculty of Mechanics and Mathematicswithout scientific degree, no status
References
- G. Freudenburg, Algebraic theory of locally nilpotent derivations, Encyclopaedia Math. Sci., 136, Invariant Theory Algebr. Transform. Groups, VII, Springer-Verlag, Berlin, 2006, xii+261 pp.
- D. Daigle, “A necessary and sufficient condition for triangulability of derivations of $k[X, Y, Z]$”, J. Pure Appl. Algebra, 113:3 (1996), 297–305
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