Pseudo-Euclidean Novikov Superalgebras: Structure and Properties
Abstract
A pseudo-Euclidean Novikov superalgebra A is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form ⟨, ⟩ such that all left multiplication operators are ⟨, ⟩-antisymmetric. In this case, the associated Lie superalgebra (A−,⟨, ⟩) 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 \emph{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 over the field of real numbers.
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BibTeX
@misc{benayadi2026pseudoeuclidean,
title = {{Pseudo-Euclidean Novikov Superalgebras: Structure and Properties}},
author = {Said Benayadi and Sofiane Bouarroudj and Hamza El Ouali},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.20775},
eprint = {2605.20775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.20775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pseudo-Euclidean Novikov Superalgebras: Structure and Properties
AU - Said Benayadi
AU - Sofiane Bouarroudj
AU - Hamza El Ouali
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.20775
UR - https://arxiv.org/abs/2605.20775
AB - A pseudo-Euclidean Novikov superalgebra A is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form ⟨, ⟩ such that all left multiplication operators are ⟨, ⟩-antisymmetric. In this case, the associated Lie superalgebra (A^−,⟨, ⟩) 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 \emph{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 over the field of real numbers.
ER -