Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 49 min ago
PreprintCC BY 4.0HAL

Locally finite solvable Lie algebras of derivations

  • M Zaidenberg
Open at sourcePDFCite

Abstract

Let X be an affine variety and h ⊂ Lie(Aut(X)) be a solvable Lie subalgebra generated by a finite collection of locally finite Lie subalgebras. The authors of [3] wondered whether h is itself locally finite. Here we present some criteria for the local finiteness of h. We also answer this question in the affirmative in the particular case where X is the affine plane A^2.

Related

  1. Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic
    Oksana Bezushchak, Anatoliy Petravchuk
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. On the Isotropy Groups of Locally Finite Derivations of Laurent Polynomial Algebras
    Anderson Porto, Marcelo Veloso
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Rigidity for Lie algebras of locally finite derivations
    Mohamed Ali Belabbas
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. On Locally Finite Derivations in Ore Extensions
    R. Baltazar, A. Bianchi, M. Veloso +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras
    Khusainboy Atajonov, Abror Khudoyberdiyev, Bakhtiyor Yusupov
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{zaidenberg2026locally,
  title = {{Locally finite solvable Lie algebras of derivations}},
  author = {M Zaidenberg},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05581963v3},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Locally finite solvable Lie algebras of derivations
AU  - M Zaidenberg
PY  - 2026
DA  - 2026/10/29
PB  - HAL
UR  - https://hal.science/hal-05581963v3
AB  - Let X be an affine variety and h ⊂ Lie(Aut(X)) be a solvable Lie subalgebra generated by a finite collection of locally finite Lie subalgebras. The authors of [3] wondered whether h is itself locally finite. Here we present some criteria for the local finiteness of h. We also answer this question in the affirmative in the particular case where X is the affine plane A^2.
ER  -