Abstract
Let (L,[p]) be a finite dimensional restricted Lie algebra over a field K of positive characteristic p. A Jordan–Chevalley–Seligman decomposition of x∈L is a unique expression of x as a sum of commuting semisimple and nilpotent elements in L. It is well-known that each x∈L has such a decomposition when K is perfect. When K is non-perfect, the present paper gives several criteria for the existence of a Jordan–Chevalley–Seligman decomposition for a given x∈L as well as for determining when an element in the restricted subalgebra generated by x is semisimple or nilpotent.
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.
