Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra

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Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra. / Khodzitskii, A.

In: Russian Mathematics, Vol. 70, No. 4, 26.07.2026, p. 21-41.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f48fa5e389fb44afb81dee979c13af8e,

title = "Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra",

abstract = "Abstract: Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota–Baxter operators are studied on the polynomial algebra. Injective Rota–Baxter operators of weight zero on were described in 2021. We classify the following classes of monomial Rota–Baxter operators of weight zero on the polynomial algebra and its augmentation ideal : (1) nonincreasing in degree that do not contain monomials in the kernel, (2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given Rota–Baxter operator and vice versa.",

keywords = "Rota–Baxter operator, averaging operator, polynomial algebra, Оператор Рота-Бакстера, оператор усреднения, полиномиальная алгебра",

author = "A. Khodzitskii",

note = "Khodzitskii, A. Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra. Russ Math. 70, 21–41 (2026). https://doi.org/10.3103/S1066369X24601169. – EDN JVWOCN. The study was supported by the Russian Science Foundation, project no. 23-71-10005, https://rscf.ru/project/23-71-10005/",

year = "2026",

month = jul,

day = "26",

doi = "10.3103/S1066369X24601169",

language = "English",

volume = "70",

pages = "21--41",

journal = "Russian Mathematics",

issn = "1066-369X",

publisher = "Allerton Press Inc.",

number = "4",

}

RIS

TY - JOUR

T1 - Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra

AU - Khodzitskii, A.

N1 - Khodzitskii, A. Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra. Russ Math. 70, 21–41 (2026). https://doi.org/10.3103/S1066369X24601169. – EDN JVWOCN. The study was supported by the Russian Science Foundation, project no. 23-71-10005, https://rscf.ru/project/23-71-10005/

PY - 2026/7/26

Y1 - 2026/7/26

N2 - Abstract: Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota–Baxter operators are studied on the polynomial algebra. Injective Rota–Baxter operators of weight zero on were described in 2021. We classify the following classes of monomial Rota–Baxter operators of weight zero on the polynomial algebra and its augmentation ideal : (1) nonincreasing in degree that do not contain monomials in the kernel, (2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given Rota–Baxter operator and vice versa.

AB - Abstract: Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota–Baxter operators are studied on the polynomial algebra. Injective Rota–Baxter operators of weight zero on were described in 2021. We classify the following classes of monomial Rota–Baxter operators of weight zero on the polynomial algebra and its augmentation ideal : (1) nonincreasing in degree that do not contain monomials in the kernel, (2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given Rota–Baxter operator and vice versa.

KW - Rota–Baxter operator

KW - averaging operator

KW - polynomial algebra

KW - Оператор Рота-Бакстера

KW - оператор усреднения

KW - полиномиальная алгебра

UR - https://www.mendeley.com/catalogue/af06796d-667e-3eea-b717-742cb89652a5/

UR - https://www.scopus.com/pages/publications/105045673987

UR - https://www.elibrary.ru/item.asp?id=91841688

U2 - 10.3103/S1066369X24601169

DO - 10.3103/S1066369X24601169

M3 - Article

VL - 70

SP - 21

EP - 41

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 4

ER -

ID: 83878178