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The construction of real Frobenius Lie algebras from non-commutative nilpotent Lie algebras of dimension
| Content Provider | Scilit |
|---|---|
| Author | Kurniadi, E. Carnia, E. Supriatna, A. K. |
| Copyright Year | 2021 |
| Description | Journal: Journal of Physics: Conference Series In this present paper, we study real Frobenius Lie algebras constructed from non-commutative nilpotent Lie algebras of dimension ≤ 4. The main purpose is to obtain Frobenius Lie algebras of dimension ≤ 6. Particularly, for a given non-commutative nilpotent Lie algebras N of dimension ≤ 4 we show that there exist commutative subalgebras of dimension ≤ 2 such that the semi-direct sums ɡ = N⊕T is Frobenius Lie algebras. Moreover, T is called a split torus which is a commutative subalgebra of derivation of N and it depends on the given N. To obtain this split torus, we apply Ayala's formulas of a Lie algebra derivation by taking a diagonal matrix of a standard representation matrix of the Lie algebra derivation of N. The discussion of higher dimension of Frobenius Lie algebras obtained from non-commutative nilpotent Lie algebras is still an open problem. |
| Related Links | https://iopscience.iop.org/article/10.1088/1742-6596/1722/1/012025/pdf |
| ISSN | 17426588 |
| e-ISSN | 17426596 |
| DOI | 10.1088/1742-6596/1722/1/012025 |
| Journal | Journal of Physics: Conference Series |
| Issue Number | 1 |
| Volume Number | 1722 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2021-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Journal of Physics: Conference Series Nilpotent Lie Frobenius Lie Algebras Commutative Nilpotent |
| Content Type | Text |
| Resource Type | Article |
| Subject | Physics and Astronomy |
