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arXiv · 1710.02377

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

Vsevolod Gubarev
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Abstract

It is proved that any Rota---Baxter operator of zero weight on Jordan algebra of a nondegenerate bilinear symmetric form is nilpotent of index less or equal three. We state exact value of nilpotency index on simple Jordan algebra of Clifford type over 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.

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Vsevolod Gubarev. 2017-10-06. Rota-Baxter operators of zero weight on simple Jordan algebra of Clifford type. https://doi.org/10.17377/semi.2017.14.131

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