Commuting 𝑈-operators in Jordan algebras

Anquela, José; Cortés, Teresa; Petersson, Holger

doi:10.1090/S0002-9947-2014-06054-6

Commuting $U$-operators in Jordan algebras
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by José A. Anquela, Teresa Cortés and Holger P. Petersson PDF

Trans. Amer. Math. Soc. 366 (2014), 5877-5902 Request permission

Abstract:

For elements $x,y$ in a non-degenerate non-unital Jordan algebra over a commutative ring, the relation $x \circ y = 0$ is shown to imply that the $U$-operators of $x$ and $y$ commute: $U_xU_y = U_yU_x$. The proof rests on the Zel$’$manov-McCrimmon classification of strongly prime quadratic Jordan algebras.

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