Rota–Baxter Operators on Quadratic Algebras

  • Pilar Benito
  • Vsevolod GubarevEmail author
  • Alexander Pozhidaev
Open Access


We prove that all Rota–Baxter operators on a quadratic division algebra are trivial. For nonzero weight, we state that all Rota–Baxter operators on the simple odd-dimensional Jordan algebra of bilinear form are projections on a subalgebra along another one. For weight zero, we find a connection between the Rota–Baxter operators and the solutions to the alternative Yang–Baxter equation on the Cayley–Dickson algebra. We also investigate the Rota–Baxter operators on the matrix algebras of order two, the Grassmann algebra of plane, and the Kaplansky superalgebra.


Rota–Baxter operator Yang–Baxter equation Quadratic algebra Grassmann algebra Jordan algebra of bilinear form Matrix algebra Kaplansky superalgebra 

Mathematics Subject Classification

Primary 17A45 Secondary 17C50 Thirdly 16T25 



Open access funding provided by Austrian Science Fund (FWF). Pilar Benito acknowledges financial support by Grant MTM2017-83506-C2-1-P (AEI/FEDER, UE). Vsevolod Gubarev is supported by the Austrian Science Foundation FWF, Grant P28079.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Universidad de La RiojaLogroñoSpain
  2. 2.University of ViennaViennaAustria
  3. 3.Sobolev Institute of MathematicsNovosibirskRussia
  4. 4.Novosibirsk State UniversityNovosibirskRussia

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