Rota–Baxter Operators on Quadratic Algebras

Pilar Benito, Vsevolod Gubarev, Alexander Pozhidaev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number189
Number of pages23
JournalMediterranean Journal of Mathematics
Volume15
Issue number5
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • Grassmann algebra
  • Jordan algebra of bilinear form
  • Kaplansky superalgebra
  • Matrix algebra
  • Quadratic algebra
  • Rota–Baxter operator
  • Yang–Baxter equation
  • Yang-Baxter equation
  • LIE BIALGEBRAS
  • Rota-Baxter operator
  • DENDRIFORM ALGEBRAS
  • EQUATION

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