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Simple finite-dimensional binary Lie superalgebras
Abstract
We prove that every complex finite-dimensional simple binary Lie superalgebra with non-zero odd part is either a simple Lie superalgebra, and hence is one of the superalgebras of Kac's list, or the two-dimensional non-Lie superalgebra B2. This confirms the Grishkov--Shestakov conjecture and, together with the theorems of Grishkov and Filippov on simple binary Lie algebras, gives the answer to Shestakov's question from the Dniester Notebook (Problem 3.100(d)) over the field of complex numbers.
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BibTeX
@misc{abdelwahab2026simple,
title = {{Simple finite-dimensional binary Lie superalgebras}},
author = {Hani Abdelwahab and Ivan Kaygorodov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30386},
eprint = {2610.30386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30386},
}
RIS
TY - UNPB
TI - Simple finite-dimensional binary Lie superalgebras
AU - Hani Abdelwahab
AU - Ivan Kaygorodov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30386
UR - https://arxiv.org/abs/2610.30386
AB - We prove that every complex finite-dimensional simple binary Lie superalgebra with non-zero odd part is either a simple Lie superalgebra, and hence is one of the superalgebras of Kac's list, or the two-dimensional non-Lie superalgebra B_2. This confirms the Grishkov--Shestakov conjecture and, together with the theorems of Grishkov and Filippov on simple binary Lie algebras, gives the answer to Shestakov's question from the Dniester Notebook (Problem 3.100(d)) over the field of complex numbers.
ER -