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Commuting $ U$-operators in Jordan algebras


Authors: José A. Anquela, Teresa Cortés and Holger P. Petersson
Journal: Trans. Amer. Math. Soc. 366 (2014), 5877-5902
MSC (2010): Primary 17C10; Secondary 20B22, 20E42, 17C40, 17C60
DOI: https://doi.org/10.1090/S0002-9947-2014-06054-6
Published electronically: July 17, 2014
MathSciNet review: 3256187
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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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Additional Information

José A. Anquela
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, E-33007 Oviedo, Spain
Email: anque@orion.ciencias.uniovi.es

Teresa Cortés
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, E-33007 Oviedo, Spain
Email: cortes@orion.ciencias.uniovi.es

Holger P. Petersson
Affiliation: Fakultät für Mathematik und Informatik, FernUniversität in Hagen, D-58084 Hagen, Germany
Email: holger.petersson@fernuni-hagen.de

DOI: https://doi.org/10.1090/S0002-9947-2014-06054-6
Received by editor(s): August 20, 2012
Received by editor(s) in revised form: December 13, 2012, and December 17, 2012
Published electronically: July 17, 2014
Additional Notes: The research of the first two authors was partially supported by the Spanish Ministerio de Economía y Competitividad and Fondos FEDER, MTM2010-16153, and MTM2013-40841-P
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.