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.

引用

页数：9

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