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Gholami, Nahid, Saeedi, Farshid. (1402). Structure, capability, Schur multiplier and tensor square of some nilpotent n-Lie algebras of class two. , (), -. doi: 10.30495/jnrm.2023.71717.2383
Nahid Gholami; Farshid Saeedi. "Structure, capability, Schur multiplier and tensor square of some nilpotent n-Lie algebras of class two". , , , 1402, -. doi: 10.30495/jnrm.2023.71717.2383
Gholami, Nahid, Saeedi, Farshid. (1402). 'Structure, capability, Schur multiplier and tensor square of some nilpotent n-Lie algebras of class two', , (), pp. -. doi: 10.30495/jnrm.2023.71717.2383
Gholami, Nahid, Saeedi, Farshid. Structure, capability, Schur multiplier and tensor square of some nilpotent n-Lie algebras of class two. , 1402; (): -. doi: 10.30495/jnrm.2023.71717.2383

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  XML
نوع مقاله: research paper
شناسه دیجیتال (DOI): 10.30495/jnrm.2023.71717.2383
نویسندگان
Nahid Gholami؛ Farshid Saeedi email
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
چکیده
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.
کلیدواژه‌ها
nilpotent n-Lie algebra؛ generalized Heisenberg؛ tensor square؛ basic commutator؛ Schur multiplier
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