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Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators. / Khodzitskii, Artem.

In: Mediterranean Journal of Mathematics, Vol. 20, No. 5, 251, 10.2023.

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

Harvard

Khodzitskii, A 2023, 'Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators', Mediterranean Journal of Mathematics, vol. 20, no. 5, 251. https://doi.org/10.1007/s00009-023-02453-8

APA

Khodzitskii, A. (2023). Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators. Mediterranean Journal of Mathematics, 20(5), [251]. https://doi.org/10.1007/s00009-023-02453-8

Vancouver

Khodzitskii A. Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators. Mediterranean Journal of Mathematics. 2023 Oct;20(5):251. doi: 10.1007/s00009-023-02453-8

Author

Khodzitskii, Artem. / Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators. In: Mediterranean Journal of Mathematics. 2023 ; Vol. 20, No. 5.

BibTeX

@article{bbf61d1d8db64f94b772b0c7bd9870ea,
title = "Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators",
abstract = "The intensive study of Rota–Baxter operators on the polynomial algebra F[x] has been started with the work of Zheng et al. (Pac J Math (2) 275:481– 507, 2015). We deal with the case of two variables and monomial Rota–Baxter operators of nonzero weight. The family of such operators arisen from homomorphic averaging operators on F[x, y] is described.",
keywords = "Rota–Baxter operator, averaging operator, decomposition of algebra, polynomial algebra",
author = "Artem Khodzitskii",
note = "The author is grateful to Vsevolod Gubarev for scientific supervision. The author is also grateful to Maxim Goncharov, Valery G. Bardakov, and the anonymous reviewer for their helpful remarks.",
year = "2023",
month = oct,
doi = "10.1007/s00009-023-02453-8",
language = "English",
volume = "20",
journal = "Mediterranean Journal of Mathematics",
issn = "1660-5446",
publisher = "Birkhauser Verlag Basel",
number = "5",

}

RIS

TY - JOUR

T1 - Monomial Rota–Baxter Operators of Nonzero Weight on F[x, y] Coming from Averaging Operators

AU - Khodzitskii, Artem

N1 - The author is grateful to Vsevolod Gubarev for scientific supervision. The author is also grateful to Maxim Goncharov, Valery G. Bardakov, and the anonymous reviewer for their helpful remarks.

PY - 2023/10

Y1 - 2023/10

N2 - The intensive study of Rota–Baxter operators on the polynomial algebra F[x] has been started with the work of Zheng et al. (Pac J Math (2) 275:481– 507, 2015). We deal with the case of two variables and monomial Rota–Baxter operators of nonzero weight. The family of such operators arisen from homomorphic averaging operators on F[x, y] is described.

AB - The intensive study of Rota–Baxter operators on the polynomial algebra F[x] has been started with the work of Zheng et al. (Pac J Math (2) 275:481– 507, 2015). We deal with the case of two variables and monomial Rota–Baxter operators of nonzero weight. The family of such operators arisen from homomorphic averaging operators on F[x, y] is described.

KW - Rota–Baxter operator

KW - averaging operator

KW - decomposition of algebra

KW - polynomial algebra

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85162246619&origin=inward&txGid=2ff922618e39ec7123725efa7dd6753b

UR - https://www.mendeley.com/catalogue/9f5fc423-58a7-3239-b479-c0280cb7e1f6/

U2 - 10.1007/s00009-023-02453-8

DO - 10.1007/s00009-023-02453-8

M3 - Article

VL - 20

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 5

M1 - 251

ER -

ID: 54027204