Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions

Abdullayeva, Shahlo

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

In this paper, we study anti-derivations, local anti-derivations and 2-local anti-derivations on several finite-dimensional complex Leibniz algebras. More precisely, we consider thenull-filiform Leibniz algebra NF n , the naturally graded non-Lie filiform Leibniz algebras F 1nand F 2n ,and their associated solvable extensions. Here, an anti-derivation is understood as a (−1)-derivationsatisfyingD([x,y]) = −[D(x),y] − [x,D(y)].We first determine the spaces of anti-derivations for all algebras under consideration. We then ob-tain complete descriptions of their local anti-derivations. In particular, every local anti-derivation isan anti-derivation precisely for the algebras R, R(F 1n ) and L 2 , whereas NF n , F1n , F2nand L 1 admitlocal anti-derivations which are not anti-derivations. Furthermore, we prove that every 2-local anti-derivation on NF n and on each of the four solvable extensions is an anti-derivation. For F 1nand F 2n ,we construct families of nonlinear 2-local anti-derivations with values in the center. The membersof these families are anti-derivations exactly when the corresponding defining maps are linear.

Maqola ma’lumotlari
MualliflarAbdullayeva, Shahlo
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-06
Jild2
Son2.3
Betlar3-15
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.69617/nuuz.v2i2.3.15231
Indeksga qo‘shilgan2026-10-07

DOI: 10.69617/nuuz.v2i2.3.15231 · Maqolaning asl sahifasi

Kalit so‘zlar

Leibniz algebras, anti-derivations, local anti-derivations, 2-local anti-derivations, fili- form algebras.

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAAbdullayeva, Shahlo (2026). Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions. Ўзбекистон Миллий университети хабарлари, 2(2.3), 3-15. https://doi.org/10.69617/nuuz.v2i2.3.15231
GOST (OAK)Abdullayeva, Shahlo Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 3-15. – DOI: 10.69617/nuuz.v2i2.3.15231.
MLAAbdullayeva, Shahlo. “Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 3-15, 2026. https://doi.org/10.69617/nuuz.v2i2.3.15231
ChicagoAbdullayeva, Shahlo. “Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 3-15 (2026). https://doi.org/10.69617/nuuz.v2i2.3.15231
HarvardAbdullayeva, Shahlo (2026) ‘Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 3-15. https://doi.org/10.69617/nuuz.v2i2.3.15231
BibTeX
@article{abdullayevashahlo2026,
  title = {Local and 2-local anti-derivations on null-filiform and filiform Leibniz algebras and their solvable extensions},
  author = {Abdullayeva, Shahlo},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {3-15},
  doi = {10.69617/nuuz.v2i2.3.15231},
  url = {https://doi.org/10.69617/nuuz.v2i2.3.15231}
}

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