On commuting U-operators in Jordan algebras

Recently J. A. Anquela, T. Cortés, and H. P. Petersson proved that for elements x, y in a non-degenerate Jordan algebra J, the relation x o y = 0 implies that the U-operators of x and y commute: U_x U_y = U_y U_x. We show that the result may be not true without the assumption on non-degeneracy of J. We give also a simpler proof of the mentioned result in the case of linear Jordan algebras, that is, when char F ≠ 2.

comuop2.pdf (72K)

I. Shestakov < ivan.shestakov@gmail.com >