Four-dimensional real division algebras with few derivations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 177-207
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In order to advance in the determination of all four-dimensional real division algebras $\mathcal{A}$, we introduce a new duplication process preserving the unit. This duplication process accompanied by an isotopy allow us to obtain all of these algebras in case $\operatorname{Der}(\mathcal{A})\neq\{0\}$ and partially in case $\operatorname{Der}(\mathcal{A})=\{0\}$. In the last case, we provide an $8$-parameter family of ugly $\mathbb C$-associative algebras and an $8$-parameter family of $\mathbb C$-associative algebras whose group of automorphisms contains only the identity and some reflections. For non-ugly algebras $\mathbb H_{f, f}$, the group $\operatorname{Aut}(\mathbb H_{f, f})$ contains a reflection. Also algebras $\mathcal A$ with $\operatorname{Aut}(\mathcal A)=\mathbb Z_2$ or $\mathbb Z_2\times\mathbb Z_2$ are studied.
@article{FPM_2021_23_4_a10,
author = {O. Fayz and E. Napedenina and A. Rochdi and M. Tvalavadze},
title = {Four-dimensional real division algebras with few derivations},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {177--207},
publisher = {mathdoc},
volume = {23},
number = {4},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a10/}
}
TY - JOUR AU - O. Fayz AU - E. Napedenina AU - A. Rochdi AU - M. Tvalavadze TI - Four-dimensional real division algebras with few derivations JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2021 SP - 177 EP - 207 VL - 23 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a10/ LA - ru ID - FPM_2021_23_4_a10 ER -
%0 Journal Article %A O. Fayz %A E. Napedenina %A A. Rochdi %A M. Tvalavadze %T Four-dimensional real division algebras with few derivations %J Fundamentalʹnaâ i prikladnaâ matematika %D 2021 %P 177-207 %V 23 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a10/ %G ru %F FPM_2021_23_4_a10
O. Fayz; E. Napedenina; A. Rochdi; M. Tvalavadze. Four-dimensional real division algebras with few derivations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 177-207. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a10/