TY - JOUR

T1 - Rota–Baxter Operators on Quadratic Algebras

AU - Benito, Pilar

AU - Gubarev, Vsevolod

AU - Pozhidaev, Alexander

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - Grassmann algebra

KW - Jordan algebra of bilinear form

KW - Kaplansky superalgebra

KW - Matrix algebra

KW - Quadratic algebra

KW - Rota–Baxter operator

KW - Yang–Baxter equation

KW - Yang-Baxter equation

KW - LIE BIALGEBRAS

KW - Rota-Baxter operator

KW - DENDRIFORM ALGEBRAS

KW - EQUATION

UR - http://www.scopus.com/inward/record.url?scp=85051635995&partnerID=8YFLogxK

U2 - 10.1007/s00009-018-1234-5

DO - 10.1007/s00009-018-1234-5

M3 - Article

AN - SCOPUS:85051635995

VL - 15

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 5

M1 - 189

ER -