(21). The Jordan Algebras of a Lie Algebra.
Autores: A. Fernández López, E. García y M. Gómez Lozano.
Revista: J. Algebra. 308, 2007, 164-177. (JCR:72 de 207. Factor de impacto 0.630)
Abstract: We attach a Jordan algebra $L_x$ to any ad-nilpotent element $x$ of index of nilpotence $\leq 3$ in a Lie algebra $L$. This Jordan algebra has a behavior 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 $x$.
r ideals. We also characterize when these algebras are Artinian, proving in particular that a finitary simple Lie algebra over an algebraically closed field of characteristic zero is Artinian if 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.