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Abstract
We show that any ad-nilpotent element x of index less than or equal to three of a Lie algebra L defines a 5-filtration in L. When L is nondegenerate, the ℤ-graded Lie algebra associated to this filtration is isomorphic to L if and only x is von Neumann regular, if and only if
is nondegenerate.
Key Words:
ACKNOWLEDGMENTS
The authors would like to thank the Prof. Antonio Fernández López and the referee for their valuable comments and suggestions.
The first author was partially supported by the MEC and Fondos FEDER MTM2010-16153, by FMQ 264, and by MICINN I3-2010/00075/001.
The second author was partially supported by the MEC and Fondos FEDER MTM2010-19482, by FMQ 264 and FQM 3737, and by MICINN I3-2010/00075/001.
Notes
Communicated by M. Bresar.