The Jordan Algebras of a Lie Algebra

We attach a Jordan algebra L_x to any ad-nilpotent element x of index of nilpotence at most 3 in a Lie algebra L. This Jordan algebra has a behaviour similar to that of the local algebra of a Jordan system at an element. Thus, L_x inherits nice properties from L and keeps relevant information about the element x.

(This paper has appeared in J. Algebra 308 (2007), 164--177)

jolie.pdf (240K)

A. Fernández López < emalfer@agt.cie.uma.es >

E. Gárcia < esther.garcia@urjc.es >

M. Gómez Lozano < magomez@agt.cie.uma.es >