Abstract
Up to conjugation by an automorphism, we describe the Rota–Baxter operators of weight zero or nonzero on the simple four-dimensional Jordan superalgebra \( D_{t} \) over an algebraically closed field of characteristic 0. The description includes the classification of all decompositions of \( D_{t} \) into a direct sum of two subalgebras.
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Acknowledgments
The authors are grateful to A. Elduque and an anonymous referee for useful comments.
Funding
The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–282 on April 5, 2022 with the Ministry of Science and Higher Education of the Russian Federation.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 4, pp. 768–782. https://doi.org/10.33048/smzh.2022.63.404
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Bolotina, T.A., Gubarev, V.Y. Rota–Baxter Operators on the Simple Jordan Superalgebra \( D_{t} \). Sib Math J 63, 637–650 (2022). https://doi.org/10.1134/S0037446622040048
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DOI: https://doi.org/10.1134/S0037446622040048