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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.20775 |
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| _version_ | 1866917515115888640 |
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| author | Benayadi, Said Bouarroudj, Sofiane Ouali, Hamza El |
| author_facet | Benayadi, Said Bouarroudj, Sofiane Ouali, Hamza El |
| contents | A pseudo-Euclidean Novikov superalgebra $A$ is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form $\langle,\rangle$ such that all left multiplication operators are $\langle,\rangle$-antisymmetric. In this case, the associated Lie superalgebra $(A^{-},$\langle,\rangle$)$ is a flat pseudo-Euclidean Lie superalgebra. In this paper, we investigate the structure of pseudo-Euclidean Novikov superalgebras. In particular, we introduce a distinguished subclass, called Milnor superalgebras, and prove that any pseudo-Euclidean Novikov superalgebra whose two-sided ideal is non-degenerate belongs to this class. We provide a method for constructing pseudo-Euclidean Novikov superalgebras.
We also introduce a double extension procedure for pseudo-Euclidean Novikov superalgebras and show that every such superalgebra with a degenerate two-sided ideal can be obtained via this method. Furthermore, we establish that any pseudo-Euclidean Novikov superalgebra is either a Milnor superalgebra or can be obtained by a sequence of double extensions starting from a Milnor superalgebra. As an application, we provide a complete classification of pseudo-Euclidean Novikov superalgebras of total dimension at most four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20775 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-Euclidean Novikov Superalgebras: Structure and Properties Benayadi, Said Bouarroudj, Sofiane Ouali, Hamza El Rings and Algebras 17A32, 17A70, 17A60, 17D25 A pseudo-Euclidean Novikov superalgebra $A$ is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form $\langle,\rangle$ such that all left multiplication operators are $\langle,\rangle$-antisymmetric. In this case, the associated Lie superalgebra $(A^{-},$\langle,\rangle$)$ is a flat pseudo-Euclidean Lie superalgebra. In this paper, we investigate the structure of pseudo-Euclidean Novikov superalgebras. In particular, we introduce a distinguished subclass, called Milnor superalgebras, and prove that any pseudo-Euclidean Novikov superalgebra whose two-sided ideal is non-degenerate belongs to this class. We provide a method for constructing pseudo-Euclidean Novikov superalgebras. We also introduce a double extension procedure for pseudo-Euclidean Novikov superalgebras and show that every such superalgebra with a degenerate two-sided ideal can be obtained via this method. Furthermore, we establish that any pseudo-Euclidean Novikov superalgebra is either a Milnor superalgebra or can be obtained by a sequence of double extensions starting from a Milnor superalgebra. As an application, we provide a complete classification of pseudo-Euclidean Novikov superalgebras of total dimension at most four. |
| title | Pseudo-Euclidean Novikov Superalgebras: Structure and Properties |
| topic | Rings and Algebras 17A32, 17A70, 17A60, 17D25 |
| url | https://arxiv.org/abs/2605.20775 |