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Injective Rota–Baxter Operators of Weight Zero on F[x]. / Gubarev, Vsevolod; Perepechko, Alexander.
в: Mediterranean Journal of Mathematics, Том 18, № 6, 267, 12.2021.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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