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Injective Rota–Baxter Operators of Weight Zero on F[x] Full article

Journal Mediterranean Journal of Mathematics
ISSN: 1660-5446 , E-ISSN: 1660-5454
Output data Year: 2021, Volume: 18, Number: 6, Article number : 267, Pages count : DOI: 10.1007/s00009-021-01909-z
Tags Additive action; Formal integration operator; Infinite transitivity; Polynomial algebra; Rota–Baxter operator
Authors Gubarev V. 1,2 , Perepechko A. 3,4,5
Affiliations
1 Sobolev Institute of Mathematics, Acad. Koptyug ave. 4, Novosibirsk, 630090, Russian Federation
2 Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russian Federation
3 Kharkevich Institute for Information Transmission Problems, 19 Bolshoy Karetny per., Moscow, 127994, Russian Federation
4 Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., Dolgoprudny, Moscow Region 141701, Russian Federation
5 National Research University Higher School of Economics, 20 Myasnitskaya ulitsa, Moscow, 101000, Russian Federation

Funding (1)

1 Sobolev Institute of Mathematics 0314-2019-0001

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. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Cite: Gubarev V. , Perepechko A.
Injective Rota–Baxter Operators of Weight Zero on F[x]
Mediterranean Journal of Mathematics. 2021. V.18. N6. 267 . DOI: 10.1007/s00009-021-01909-z WOS Scopus OpenAlex
Identifiers:
Web of science: WOS:000714933300001
Scopus: 2-s2.0-85118718835
OpenAlex: W3212678825
Citing:
DB Citing
Scopus 1
OpenAlex 1
Web of science 1
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