PreprintCC BY 4.0arXiv
On the Classification of Nilpotent Lie Superalgebras over Fields of Characteristic 2
Abstract
The salient result of this paper is the complete classification of all nilpotent Lie superalgebras in dimensions up to four over an algebraically closed field of characteristic 2. Our method adapts the Skjelbred-Sund method to show that every n-dimensional nilpotent Lie superalgebra arises as a one-dimensional central extension of an (n-1)-dimensional one, and determines precisely when two such extensions yield isomorphic superalgebras. Carrying out this construction for dimensions up to 4, we obtain a finite, non-redundant list of pairwise non-isomorphic examples.
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BibTeX
@misc{haroon2026classification,
title = {{On the Classification of Nilpotent Lie Superalgebras over Fields of Characteristic 2}},
author = {Muhammad Uzair Haroon},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.14523},
eprint = {2611.14523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.14523},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Classification of Nilpotent Lie Superalgebras over Fields of Characteristic 2
AU - Muhammad Uzair Haroon
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.14523
UR - https://arxiv.org/abs/2611.14523
AB - The salient result of this paper is the complete classification of all nilpotent Lie superalgebras in dimensions up to four over an algebraically closed field of characteristic 2. Our method adapts the Skjelbred-Sund method to show that every n-dimensional nilpotent Lie superalgebra arises as a one-dimensional central extension of an (n-1)-dimensional one, and determines precisely when two such extensions yield isomorphic superalgebras. Carrying out this construction for dimensions up to 4, we obtain a finite, non-redundant list of pairwise non-isomorphic examples.
ER -