(22). An elemental characterization of strong primeness in Lie algebras.
Autores: E. García y M. Gómez Lozano.
Revista: J. Algebra 312, 2007, 132–141. (JCR:72 de 207. Factor de impacto 0.630)
Abstract: In this paper we prove that a Lie algebra $L$ is strongly prime if and only if $[x,[y,L]]\ne 0$ 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 $\{x,T,y\}\ne 0$ 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.
and only if it is finite dimensional. Because it is useful for our approach, we provide a characterization of the trace of a finite rank operator on a vector space over a division algebra which is intrinsic in the sense that it avoids imbeddings into finite matrices.