Nilpotent n-Lie algebras.

摘要

In 1986, Kasymov introduced the concept of nilpotent n-Lie algebras, proved an analogue of Engel's Theorem and later proved an analog of Jacobson's refinement of Engel's Theorem. Despite these achievements, the subject of nilpotency in n-Lie algebras has not been examined in great detail in the literature since. We shall explore the concept of nilpotent n-Lie algebras by examining, and proving where possible, other classical nilpotent group theory and nilpotent Lie algebra results, in the n-Lie algebra setting.