Inner ideals of the Lie algebra of the skew elements of centrally
closed prime algebras with a ring involution
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 algebras with a
ring involution over a field of characteristic not 2 or 3. 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
been described only in geometric terms. Our main tool is a theorem by
Martindale and Miers on nilpotent inner derivations of the skew-symmetric
elements of prime rings with involution.
(This paper has appeared in Proc. Amer. Math. Soc. 14(7) (2016),
2741-2751. A third coauthor is now Miguel Gómez Lozano)
Jose Brox < brox@agt.cie.uma.es >
Antonio Fernández López < emalfer@uma.es >