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Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators. / Лубков, Роман Алексеевич; Ширинговский, Илья Александрович.

в: Communications in Mathematics, Том 34, № 1, 14, 19.06.2026.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Лубков, РА & Ширинговский, ИА 2026, 'Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators', Communications in Mathematics, Том. 34, № 1, 14. https://doi.org/10.46298/cm.18245

APA

Лубков, Р. А., & Ширинговский, И. А. (2026). Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators. Communications in Mathematics, 34(1), [14]. https://doi.org/10.46298/cm.18245

Vancouver

Лубков РА, Ширинговский ИА. Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators. Communications in Mathematics. 2026 Июнь 19;34(1). 14. https://doi.org/10.46298/cm.18245

Author

Лубков, Роман Алексеевич ; Ширинговский, Илья Александрович. / Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators. в: Communications in Mathematics. 2026 ; Том 34, № 1.

BibTeX

@article{1a5b8ca967d141b7b4d75630315d8c2d,
title = "Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators",
abstract = "In this paper, we provide a comprehensive study of the structural properties of the transposed Poisson algebra W(a, −1). We classify several types of linear maps, including derivations, local derivations, quasi-derivations, and δ-derivations, showing that non-trivial δ-derivations exist only for δ = 1 and δ =1 . Furthermore, we describe the groups of automorphisms, local automorphisms, 2-local 2 automorphisms, and quasi-automorphisms. We also investigate Rota–Baxter operators of weight 1 on W(a, −1). Specifically, we classify operators that are homogeneous with respect to both the standard Z-grading and a Z2-grading, establishing a rigidity result for the latter case. Finally, we classify all W-compatible Novikov–Poisson structures, demonstrating that the associative product on the Witt algebra is universally compatible with its known Novikov structures.",
keywords = "Novikov–Poisson structure, Poisson algebra, Rota–Baxter operator, Witt algebra, automor-phism, derivation, transposed Poisson algebra, δ-derivation",
author = "Лубков, {Роман Алексеевич} and Ширинговский, {Илья Александрович}",
year = "2026",
month = jun,
day = "19",
doi = "10.46298/cm.18245",
language = "English",
volume = "34",
journal = "Communications in Mathematics",
issn = "1804-1388",
publisher = "De Gruyter",
number = "1",

}

RIS

TY - JOUR

T1 - Transposed Poisson structure on the Witt-type algebra W(a, −1): derivations, automorphisms, and Rota–Baxter operators

AU - Лубков, Роман Алексеевич

AU - Ширинговский, Илья Александрович

PY - 2026/6/19

Y1 - 2026/6/19

N2 - In this paper, we provide a comprehensive study of the structural properties of the transposed Poisson algebra W(a, −1). We classify several types of linear maps, including derivations, local derivations, quasi-derivations, and δ-derivations, showing that non-trivial δ-derivations exist only for δ = 1 and δ =1 . Furthermore, we describe the groups of automorphisms, local automorphisms, 2-local 2 automorphisms, and quasi-automorphisms. We also investigate Rota–Baxter operators of weight 1 on W(a, −1). Specifically, we classify operators that are homogeneous with respect to both the standard Z-grading and a Z2-grading, establishing a rigidity result for the latter case. Finally, we classify all W-compatible Novikov–Poisson structures, demonstrating that the associative product on the Witt algebra is universally compatible with its known Novikov structures.

AB - In this paper, we provide a comprehensive study of the structural properties of the transposed Poisson algebra W(a, −1). We classify several types of linear maps, including derivations, local derivations, quasi-derivations, and δ-derivations, showing that non-trivial δ-derivations exist only for δ = 1 and δ =1 . Furthermore, we describe the groups of automorphisms, local automorphisms, 2-local 2 automorphisms, and quasi-automorphisms. We also investigate Rota–Baxter operators of weight 1 on W(a, −1). Specifically, we classify operators that are homogeneous with respect to both the standard Z-grading and a Z2-grading, establishing a rigidity result for the latter case. Finally, we classify all W-compatible Novikov–Poisson structures, demonstrating that the associative product on the Witt algebra is universally compatible with its known Novikov structures.

KW - Novikov–Poisson structure

KW - Poisson algebra

KW - Rota–Baxter operator

KW - Witt algebra

KW - automor-phism

KW - derivation

KW - transposed Poisson algebra

KW - δ-derivation

UR - https://www.mendeley.com/catalogue/5db19373-5dcc-3741-bddf-260f67bfc673/

U2 - 10.46298/cm.18245

DO - 10.46298/cm.18245

M3 - Article

VL - 34

JO - Communications in Mathematics

JF - Communications in Mathematics

SN - 1804-1388

IS - 1

M1 - 14

ER -

ID: 158815998