An elemental characterization of strong primeness in Lie algebras

In this paper we prove that a Lie algebra L is strongly prime if and only if [x,[y,L]] is nonzero for every nonzero elements x,y in L. As a consequence, we give an elementary proof, without the classification theorem of strongly prime Jordan algebras, that a linear Jordan algebra or Jordan pair T is strongly prime if and only if {x,T,y} is nonzero for every x,y in T. Moreover, we prove that the Jordan algebras at nonzero Jordan elements of strongly prime Lie algebras are strongly prime.

strprlie.pdf (154K)

(This paper has appeared in J. Algebra 312 (2007), no. 1, 132--141)

E. García < esther.garcia@urjc.es >

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