Composition algebras and their automorphisms
Composition algebras and their automorphisms
复制标题
复合代数及其自同构
DOI：
10.1007/978-1-4612-3694-8_24
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发表时间：
1958
影响因子：
1
通讯作者：
N. Jacobson
中科院分区：
文献类型：
--
作者：
N. Jacobson
本文的主要目的是研究复合代数的自同构和自同构群，即由允许复合的二次型产生的代数。这些代数主要是四元数代数和Cayley代数。问题的确定二次形式，允许组成（Huryitz的问题）已处理的许多作者（2）。尽管如此，在任何一个地方都没有出现这个问题的最一般形式的完整解--这相当于确定任意域的代数，而不仅仅是确定可能的维数。我们在这里给出了这样的解决方案的情况下，特征不二。除了其内在的利益和应用到其他领域（例如约旦代数，绝对值代数），我们还有另一个原因治疗的Hurvitz问题再次，即：分析的组成代数是必不可少的，我们的研究，其自同构。
The principal objective of the present paper is the study of the automorphisms and groups of automorphisms of composition algebras, that is, the algebras arising from quadratic forms which permit composition. These algebras are mainly quaternion algebras and Cayley algebras. The problem of determining the quadratic forms which permit composition (Huryitz’s problem) has been treated by many authors (2). In spite of this, there does not appear in any one place a complete solution of this problem in its most general form — which amounts to the determination of the algebras for an arbitrary field and not just to the determination of the possible dimensionalities. We give such a solution here for the case of characteristic not two. Aside from its intrinsic interest and applications to other fields (for example Jordan algebras, absolute valued algebras) we have still another reason for treating the Hurvitz problem again, namely: The analysis of the composition algebras is essential for our study of their automorphisms.