|تعداد مشاهده مقاله||24,216,617|
|تعداد دریافت فایل اصل مقاله||22,099,143|
Structure, capability, Schur multiplier and tensor square of some nilpotent n-Lie algebras of class two
|Journal of New Researches in Mathematics|
|مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 آبان 1402|
|نوع مقاله: research paper|
|شناسه دیجیتال (DOI): 10.30495/jnrm.2023.71717.2383|
|Nahid Gholami؛ Farshid Saeedi|
|Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.|
|In 1985, Filippov introduced the concept of n-Lie (Filippov) algebras,|
Clearly, such an algebra becomes an ordinary Lie algebra when n=2. Beside presenting
many examples of n-Lie algebras, he also extended the notions of simplicity and nilpotency
and determined all (n+1)-dimensional n-Lie algebras over an algebraically closed field of
characteristic zero. The study of n-Lie algebras is important, since it is related to geometry and physics.
Among other results, n-Lie algebras are classified in some cases. For example, Bai et al.
classified all n-Lie algebras of dimension n+1over a field of characteristic 2. Also, they
showed that there is no simple n-Lie algebra of dimension n+2. Then, Bai et al. classified
n-Lie algebras of dimension n+2 on the algebraically closed fields with characteristic zero.
An important category of n-Lie algebras of class two, which plays an essential role in classification of nilpotent n-Lie algebras, are algebras whose derived and center are equal. We call an n-Lie algebra A, a generalized Heisenberg of rank k, if A^2=Z(A) and dimA^2=k. The classification of some generalized Heisenberg n-algebras of rank 1, 2 and 3 has been done by the second author.
In this paper, we are going to obtain the representation and the Schur multiplier of the generalized Heisenberg n-Lie algebras with maximal rank. Moreover, we calculate the tensor square and Schur multiplier of some nilpotent n-Lie algebras of class two.
|nilpotent n-Lie algebra؛ generalized Heisenberg؛ tensor square؛ basic commutator؛ Schur multiplier|
تعداد مشاهده مقاله: 32