Rota--Baxter operators of weight zero on simple Jordan algebra of Clifford type

V. Yu. Gubarev

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1524-1532

Résumé

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.

Détail

Keywords: Rota–Baxter operator, Jordan algebra of Clifford type, quadratic residue, Chevalley–Warning theorem.