Quasi-derivations of Block Lie algebras ℬ(q)

@misc{kaygorodov2026quasiderivations,
  title = {{Quasi-derivations of Block Lie algebras $\mathcalB(q)$}},
  author = {Ivan Kaygorodov and Abror Khudoyberdiyev and Zarina Shermatova},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12481},
  eprint = {2610.12481},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12481},
  note = {CC0},
}

TY  - UNPB
TI  - Quasi-derivations of Block Lie algebras ℬ(q)
AU  - Ivan Kaygorodov
AU  - Abror Khudoyberdiyev
AU  - Zarina Shermatova
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.12481
UR  - https://arxiv.org/abs/2610.12481
AB  - We compute quasi-derivations of Block Lie algebras ℬ(q). In particular, we prove that ℬ(q) has various nontrivial quasi-derivations, i.e., quasi-derivations different from derivations and δ-derivations. As corollaries, we obtain a complete description of δ-derivations, δ-biderivations, and transposed δ-Poisson structures on ℬ(q) for δ∉{0;1}. In particular, for δ∉{0;1}, ℬ(q) up to isomorphism admits only one nontrivial transposed δ-Poisson structure if q∈ℤ, and ℬ(q) does not admit nontrivial transposed δ-Poisson structures if q∉ℤ.
ER  -