On the dimension of c-nilpotent multiplier of n-Lie algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916455499431936 |
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| author | Saeedi, Farshid Akbarossadat, Seyedeh Nafiseh |
| author_facet | Saeedi, Farshid Akbarossadat, Seyedeh Nafiseh |
| contents | Let L be a finite-dimensional n-Lie algebra with free presentation F/R. Then the concept of c-nilpotent multiplier of L, denoted by M(c)(L), is defined as follows: M(c)(L) =(gamma c+1(F) R)/gamma c+1(R, F, . . . , F). In this paper, we obtain some inequalities and certain bounds for the dimension of M(c)(L) by using the basic commutators. Also, we discuss the relationship between the dimension of the c-nilpotent multiplier of L and the c-nilpotent multiplier of some factor of L. We further obtain an inequality between dimensions of c-nilpotent multiplier of n-Lie algebra and non-abelian tensor (exterior) product of a central ideal by its abelianized factor n-Lie algebra. Finally, we also determine the dimension and structure of c-nilpotent multipliers Heisenberg n-Lie algebras, which can be a useful tool for determining the dimension of the multiplier of nilpotent n-Lie algebras of class 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the dimension of c-nilpotent multiplier of n-Lie algebras Saeedi, Farshid Akbarossadat, Seyedeh Nafiseh Rings and Algebras Let L be a finite-dimensional n-Lie algebra with free presentation F/R. Then the concept of c-nilpotent multiplier of L, denoted by M(c)(L), is defined as follows: M(c)(L) =(gamma c+1(F) R)/gamma c+1(R, F, . . . , F). In this paper, we obtain some inequalities and certain bounds for the dimension of M(c)(L) by using the basic commutators. Also, we discuss the relationship between the dimension of the c-nilpotent multiplier of L and the c-nilpotent multiplier of some factor of L. We further obtain an inequality between dimensions of c-nilpotent multiplier of n-Lie algebra and non-abelian tensor (exterior) product of a central ideal by its abelianized factor n-Lie algebra. Finally, we also determine the dimension and structure of c-nilpotent multipliers Heisenberg n-Lie algebras, which can be a useful tool for determining the dimension of the multiplier of nilpotent n-Lie algebras of class 2. |
| title | On the dimension of c-nilpotent multiplier of n-Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2304.06882 |