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arXiv · 1502.07904

On commuting $U$-operators in Jordan algebras

Ivan Shestakov
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Abstract

Recently J.A.Anquela, T.Cort\'es, and H.Petersson proved that for elements $x, y$ in a non-degenerate Jordan algebra $J$, the relation $x \circ y = 0$ implies that the $U$-operators of $x$ and $y$ commute: $U_xU_y = U_yU_x$. We show that the result may be not true without the assumption on non-degeneracity of $J$. We give also a more simple proof of the mentioned result in the case of linear Jordan algebras, that is, when $char\, F\neq 2$.

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Ivan Shestakov. 2015-02-27. On commuting $U$-operators in Jordan algebras. https://arxiv.org/abs/1502.07904

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