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

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 non...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2021-12, Vol.18 (6), Article 267
Main Authors: Gubarev, Vsevolod, Perepechko, Alexander
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication
Operators (mathematics)
Polynomials
Set theory
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Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01909-z