Four-Dimensional Real Division Algebras with Few Derivations

被引：0
|
作者：
Fayz O. [1 ]
Napedenina E. [2 ]
Rochdi A. [1 ]
Tvalavadze M. [3 ]
机构：
[1] Département de Mathématiques et Informatique, Faculté des Sciences Ben M’Sik, Université Hassan II, Casablanca
[2] Plekhanov Russian University of Economics, Moscow
[3] Department of Mathematical and Computational Sciences, University of Toronto Mississauga, 3359 Mississauga Road N, Mississauga, L5L 1C6, ON
来源：
Journal of Mathematical Sciences | 2023年 / 269卷 / 4期
关键词：
D O I：
10.1007/s10958-023-06301-8
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学科分类号：
摘要：
In order to advance in the determination of all four-dimensional real division algebras 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 Der(𝒜) = {0} and partially in case Der(𝒜) = {0}. In the last case, we provide an 8-parameter family of ugly ℂ-associative algebras and an 8-parameter family of ℂ-associative algebras whose group of automorphisms contains only the identity and some reflections. For non-ugly algebras ℍf,f, the group Aut(ℍf,f) contains a reflection. Also algebras 𝒜 with Aut(𝒜) = ℤ2 or ℤ2× ℤ2 are studied. © 2023, Springer Nature Switzerland AG.
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页码：568 / 590
页数：22
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