episciences.org_10193_1675651525
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episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Communications in Mathematics
23361298
10
28
2022
Volume 30 (2022), Issue 2...
Computing subalgebras and $\mathbb{Z}_2$gradings of simple Lie algebras over finite fields
Bettina
Eick
Tobias
Moede
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).
10
28
2022
10193
https://arxiv.org/licenses/nonexclusivedistrib/1.0
arXiv:2205.03155
10.48550/arXiv.2205.03155
10.46298/cm.10193
https://cm.episciences.org/10193

https://cm.episciences.org/10193/pdf

https://cm.episciences.org/10193/pdf