A note on division algebras of dimension four

被引：2
|
作者：
Tvalavadze, Marina [1 ]
Vickery, Patrick [1 ]
机构：
[1] Univ Toronto, Dept Math & Computat Sci, 3359 Mississauga Rd N, Mississauga, ON L5L 1C6, Canada
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2017年 / 16卷 / 05期
关键词：
Real division algebras; derivation quaternion algebra; group action; quaternion group; derivation algebra;
D O I：
10.1142/S0219498817500955
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider a four-dimensional real algebra A and prove that if the quaternion group acts on a certain subset of End(A) transitively, then A is a division algebra. We will also show that under certain technical conditions A has no identity. Using these results we can explicitly construct a 16-parameter family of four-dimensional real division algebras. In addition, we will find a one-parameter family of such algebras with trivial derivation algebras.
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页数：9
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