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

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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.

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Acknowledgements

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.

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  1. Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia

    Artem Khodzitskii

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

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  • DOI: https://doi.org/10.1007/s00009-023-02453-8

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