Nilpotent N-Lie Algebras

Nilpotent;N-Lie;Frattini;Algebra

Williams, Michael Peretzian ; Dr. Ernie Stitzinger, Committee Chair,Williams, Michael Peretzian ; Dr. Ernie Stitzinger ; Committee Chair

University:North Carolina State University

关键词: Nilpotent;    N-Lie;    Frattini;    Algebra;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5772/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 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.