2025/02/26 by Gubarev, Vsevolod, Panasenko, Alexander
#16W99 #17C20 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2502.18866
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\colon R→ -R-λid, a symmetrized Rota-Baxter operator of weight λ on M2(F).