Geodesic
Rota--Baxter operators of weight zero on simple Jordan algebra of Clifford type
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1524-1532.

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It is proved that every Rota–Baxter operator of weight zero on the Jordan algebra of a nondegenerate bilinear symmetric form is nilpotent of index less or equal three. We found exact value of nilpotency index of Rota–Baxter operators of weight zero on simple Jordan algebra of Clifford type over the fields $\mathbb{R}$, $\mathbb{C}$, and $\mathbb{Z}_p$. For $\mathbb{Z}_p$, we essentially use the results from number theory concerned quadratic residues and Chevalley–Warning theorem.
Keywords: Rota–Baxter operator, Jordan algebra of Clifford type, quadratic residue, Chevalley–Warning theorem. 
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     title = {Rota--Baxter operators of weight zero on simple {Jordan} algebra of {Clifford} type},
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V. Yu. Gubarev. Rota--Baxter operators of weight zero on simple Jordan algebra of Clifford type. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1524-1532. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a46/

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