(11). 3-Graded  Lie Algebras With Jordan Finiteness Conditions.

Autores: A. Fernández López, E. García and M. Gómez Lozano. 

Revista: Communications in Algebra. 32(10), (2004), 3807-3824.   (JCR: 117 de 180. Factor de impacto: 0.350)

Abstract: A notion of socle is introduced for 3-graded Lie algebras (over a ring of scalars $\Phi$ containing ${1\over 6}$) whose associated Jordan pairs are non-degenerate. The socle turns out to be a 3-graded ideal and is the sum of some minimal 3-graded inner ideals, each of which being a central extension of the TKK-algebra of a division Jordan pair. Non-degenerate 3-graded Lie algebras having a large socle are essentially determined by TKK-algebras of simple Jordan pairs with minimal inner ideals and their derivation algebras, which are also 3-graded. Classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space provide a source of examples of infinite dimensional strongly prime 3-graded Lie algebras with non-zero socle. Other examples can be found inside the class of finitary simple Lie algebras.