Rota-Baxter operators on a six-dimensional simple Leibniz algebra

Askarov, Jandos, Kurbanbaev, Tuuelbay

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

We study Rota-Baxter operators of weight zero on a six-dimensional simple Leibnizalgebra whose associated Lie algebra is sl 2 (C) and whose Leibniz kernel is the three-dimensionalirreducible sl 2 -module V (2). Using a fixed module isomorphism between the Lie part and theLeibniz kernel, we represent an arbitrary linear operator in block form and reduce the Rota-Baxteridentity to a system of operator equations on sl 2 . We completely describe the case in which the blockmapping the Leibniz kernel to the Lie part vanishes. When the Lie component is zero, we obtainan intrinsic description of all admissible operators in terms of the Killing form. For a nonzero Liecomponent, we use the known classification of weight-zero Rota–Baxter operators on sl 2 to determinethe compatible remaining blocks and the dimensions of the corresponding solution spaces. Severalexceptional parameter values at which these dimensions increase are also identified. The cases inwhich the block from the Leibniz kernel to the Lie part is nonzero are left for further investigation.

Maqola ma’lumotlari
MualliflarAskarov, Jandos, Kurbanbaev, Tuuelbay
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-06
Jild2
Son2.3
Betlar26-36
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.69617/nuuz.v2i2.3.15233
Indeksga qo‘shilgan2026-10-07

DOI: 10.69617/nuuz.v2i2.3.15233 · Maqolaning asl sahifasi

Kalit so‘zlar

Leibniz algebra, simple Leibniz algebra, Rota-Baxter operator, sl 2 -module, Killing form.

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAAskarov, Jandos, & Kurbanbaev, Tuuelbay (2026). Rota-Baxter operators on a six-dimensional simple Leibniz algebra. Ўзбекистон Миллий университети хабарлари, 2(2.3), 26-36. https://doi.org/10.69617/nuuz.v2i2.3.15233
GOST (OAK)Askarov, Jandos, Kurbanbaev, Tuuelbay Rota-Baxter operators on a six-dimensional simple Leibniz algebra // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 26-36. – DOI: 10.69617/nuuz.v2i2.3.15233.
MLAAskarov, Jandos, and Kurbanbaev, Tuuelbay. “Rota-Baxter operators on a six-dimensional simple Leibniz algebra.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 26-36, 2026. https://doi.org/10.69617/nuuz.v2i2.3.15233
ChicagoAskarov, Jandos, and Kurbanbaev, Tuuelbay. “Rota-Baxter operators on a six-dimensional simple Leibniz algebra.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 26-36 (2026). https://doi.org/10.69617/nuuz.v2i2.3.15233
HarvardAskarov, Jandos, and Kurbanbaev, Tuuelbay (2026) ‘Rota-Baxter operators on a six-dimensional simple Leibniz algebra’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 26-36. https://doi.org/10.69617/nuuz.v2i2.3.15233
BibTeX
@article{askarovjandos2026,
  title = {Rota-Baxter operators on a six-dimensional simple Leibniz algebra},
  author = {Askarov, Jandos and Kurbanbaev, Tuuelbay},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {26-36},
  doi = {10.69617/nuuz.v2i2.3.15233},
  url = {https://doi.org/10.69617/nuuz.v2i2.3.15233}
}

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