Abstract
A notion of socle is introduced for 3-graded Lie algebras (over a ring of scalars Φ containing ) whose associated Jordan pairs are non-degenerate. The socle turns out to be a 3-graded ideal and is the sum of minimal 3-graded inner ideals each of which is 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 within the class of finitary simple Lie algebras
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
