Skew-adjoint maps and quadratic Lie algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914960441868288 |
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| author | Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge |
| author_facet | Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge |
| contents | The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any arbitrary field $\mbK$. Starting from basic structural properties of such algebras and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras in the class with quadratic dimension 2. This will enable us to recover the well-known classification of real oscillator algebras, also known as Lorentzian algebras, given by Alberto Medina in 1985. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skew-adjoint maps and quadratic Lie algebras Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge Rings and Algebras 17A45, 17B05, 17B40, 15A21 The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any arbitrary field $\mbK$. Starting from basic structural properties of such algebras and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras in the class with quadratic dimension 2. This will enable us to recover the well-known classification of real oscillator algebras, also known as Lorentzian algebras, given by Alberto Medina in 1985. |
| title | Skew-adjoint maps and quadratic Lie algebras |
| topic | Rings and Algebras 17A45, 17B05, 17B40, 15A21 |
| url | https://arxiv.org/abs/2401.03100 |