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PreprintCC BY 4.0arXiv

Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic

  • Oksana Bezushchak
  • Anatoliy Petravchuk
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Abstract

Let F be a field of positive characteristic, and let A be a finitely generated commutative associative F-algebra. We study Lie subalgebras of Der A generated by locally finite derivations. We prove that if all commutators of the generators satisfy a natural local finiteness condition, then the associative subalgebra of EndF A generated by these derivations is finite-dimensional.

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Cite

BibTeXRIS
BibTeX
@misc{bezushchak2026algebras,
  title = {{Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic}},
  author = {Oksana Bezushchak and Anatoliy Petravchuk},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15731},
  eprint = {2610.15731},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15731},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic
AU  - Oksana Bezushchak
AU  - Anatoliy Petravchuk
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15731
UR  - https://arxiv.org/abs/2610.15731
AB  - Let F be a field of positive characteristic, and let A be a finitely generated commutative associative F-algebra. We study Lie subalgebras of Der A generated by locally finite derivations. We prove that if all commutators of the generators satisfy a natural local finiteness condition, then the associative subalgebra of End_F A generated by these derivations is finite-dimensional.
ER  -