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Inner ideals of Lie algebras of skew elements of prime rings with involution


Authors: Jose Brox, Antonio Fernández López and Miguel Gómez Lozano
Journal: Proc. Amer. Math. Soc. 144 (2016), 2741-2751
MSC (2010): Primary 17B60; Secondary 16W10, 17C50
DOI: https://doi.org/10.1090/proc/12903
Published electronically: March 22, 2016
MathSciNet review: 3487211
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Abstract: In this note we extend the Lie inner ideal structure of simple Artinian rings with involution, initiated by Benkart and completed by Benkart and Fernández López, to centrally closed prime rings with involution of characteristic not $ 2$, $ 3$ or $ 5$. New Lie inner ideals (which we call special) occur when making this extension. We also give a purely algebraic description of the so-called Clifford inner ideals, which had only been described in geometric terms.


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Additional Information

Jose Brox
Affiliation: Departamento de álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain
Email: brox@agt.cie.uma.es

Antonio Fernández López
Affiliation: Departamento de álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain
Email: emalfer@uma.es

Miguel Gómez Lozano
Affiliation: Departamento de álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain
Email: magomez@agt.cie.uma.es

DOI: https://doi.org/10.1090/proc/12903
Keywords: Inner ideals, Lie algebras, associative algebras with involution
Received by editor(s): April 23, 2014
Published electronically: March 22, 2016
Additional Notes: The first author was supported by the Spanish MEC through the FPU grant AP2009-4848, and by the Junta de Andalucía FQM264.
The second author was supported by the Spanish MEC and Fondos FEDER, MTM2010-19482.
The third author was supported by the Spanish MEC and Fondos FEDER, MTM2010-19482, and by the Junta de Andalucía FQM264.
Dedicated: Dedicated to Professor W. S. Martindale, 3rd.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society

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