TY - JOUR

T1 - Rota—Baxter operators on the simple Jordan algebra of matrices of order two

AU - Gubarev, Vsevolod

AU - Panasenko, Alexander

N1 - The authors are grateful to V.N. Zhelyabin and P.S. Kolesnikov for the helpful discussions. The study was supported by a grant from the Russian Science Foundation No 23-71-10005, https://rscf.ru/project/23-71-10005/.

PY - 2025/7/17

Y1 - 2025/7/17

N2 - We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a∘b=(ab+ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota—Baxter operator of weight λ on M2(F) or is, up to the action of ϕ:R→-R-λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).

AB - We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a∘b=(ab+ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota—Baxter operator of weight λ on M2(F) or is, up to the action of ϕ:R→-R-λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).

KW - Jordan algebra

KW - Rota—Baxter operator

KW - matrix algebra

UR - https://www.mendeley.com/catalogue/21254f2a-64a7-306b-9b51-0e15607309ac/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105011051466&origin=inward

U2 - 10.1007/s40840-025-01932-3

DO - 10.1007/s40840-025-01932-3

M3 - Article

VL - 48

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 5

M1 - 147

ER -