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Injective Rota–Baxter Operators of Weight Zero on F[x]. / Gubarev, Vsevolod; Perepechko, Alexander.

In: Mediterranean Journal of Mathematics, Vol. 18, No. 6, 267, 12.2021.

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

Harvard

Gubarev, V & Perepechko, A 2021, 'Injective Rota–Baxter Operators of Weight Zero on F[x]', Mediterranean Journal of Mathematics, vol. 18, no. 6, 267. https://doi.org/10.1007/s00009-021-01909-z

APA

Gubarev, V., & Perepechko, A. (2021). Injective Rota–Baxter Operators of Weight Zero on F[x]. Mediterranean Journal of Mathematics, 18(6), [267]. https://doi.org/10.1007/s00009-021-01909-z

Vancouver

Gubarev V, Perepechko A. Injective Rota–Baxter Operators of Weight Zero on F[x]. Mediterranean Journal of Mathematics. 2021 Dec;18(6):267. doi: 10.1007/s00009-021-01909-z

Author

Gubarev, Vsevolod ; Perepechko, Alexander. / Injective Rota–Baxter Operators of Weight Zero on F[x]. In: Mediterranean Journal of Mathematics. 2021 ; Vol. 18, No. 6.

BibTeX

@article{e5b9fa82a95c4aa38c8c12ca1ae22edf,
title = "Injective Rota–Baxter Operators of Weight Zero on F[x]",
abstract = "Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota–Baxter operator of weight zero on the polynomial algebra R[x] is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.",
keywords = "Additive action, Formal integration operator, Infinite transitivity, Polynomial algebra, Rota–Baxter operator",
author = "Vsevolod Gubarev and Alexander Perepechko",
note = "Funding Information: Vsevolod Gubarev is supported by the Program of fundamental scientific researches of the Siberian Branch of Russian Academy of Sciences, I.1.1, project 0314-2019-0001. The research of Alexander Perepechko was supported by the grant RSF-19-11-00172. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",
year = "2021",
month = dec,
doi = "10.1007/s00009-021-01909-z",
language = "English",
volume = "18",
journal = "Mediterranean Journal of Mathematics",
issn = "1660-5446",
publisher = "Birkhauser Verlag Basel",
number = "6",

}

RIS

TY - JOUR

T1 - Injective Rota–Baxter Operators of Weight Zero on F[x]

AU - Gubarev, Vsevolod

AU - Perepechko, Alexander

N1 - Funding Information: Vsevolod Gubarev is supported by the Program of fundamental scientific researches of the Siberian Branch of Russian Academy of Sciences, I.1.1, project 0314-2019-0001. The research of Alexander Perepechko was supported by the grant RSF-19-11-00172. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2021/12

Y1 - 2021/12

N2 - Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota–Baxter operator of weight zero on the polynomial algebra R[x] is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.

AB - Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota–Baxter operator of weight zero on the polynomial algebra R[x] is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.

KW - Additive action

KW - Formal integration operator

KW - Infinite transitivity

KW - Polynomial algebra

KW - Rota–Baxter operator

UR - http://www.scopus.com/inward/record.url?scp=85118718835&partnerID=8YFLogxK

U2 - 10.1007/s00009-021-01909-z

DO - 10.1007/s00009-021-01909-z

M3 - Article

AN - SCOPUS:85118718835

VL - 18

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 6

M1 - 267

ER -

ID: 34642351