10.46298/cm.10193
https://cm.episciences.org/10193
Eick, Bettina
Bettina
Eick
Moede, Tobias
Tobias
Moede
Computing subalgebras and $\mathbb{Z}_2$-gradings of simple Lie algebras over finite fields
This paper introduces two new algorithms for Lie algebras over finite fields
and applies them to the investigate the known simple Lie algebras of dimension
at most $20$ over the field $\mathbb{F}_2$ with two elements. The first
algorithm is a new approach towards the construction of $\mathbb{Z}_2$-gradings
of a Lie algebra over a finite field of characteristic $2$. Using this, we
observe that each of the known simple Lie algebras of dimension at most $20$
over $\mathbb{F}_2$ has a $\mathbb{Z}_2$-grading and we determine the
associated simple Lie superalgebras. The second algorithm allows us to compute
all subalgebras of a Lie algebra over a finite field. We apply this to compute
the subalgebras, the maximal subalgebras and the simple subquotients of the
known simple Lie algebras of dimension at most $16$ over $\mathbb{F}_2$ (with
the exception of the $15$-dimensional Zassenhaus algebra).
episciences.org
Mathematics - Rings and Algebras
17B05, 17B50, 17B70, 17-08
arXiv.org - Non-exclusive license to distribute
2022-10-26
2022-10-28
2022-10-28
eng
journal article
arXiv:2205.03155
10.48550/arXiv.2205.03155
2336-1298
https://cm.episciences.org/10193/pdf
VoR
application/pdf
Communications in Mathematics
Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
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