An Embedding Theorem for Reduced Albert Algebras Over Arbitrary Fields
An Embedding Theorem for Reduced Albert Algebras Over Arbitrary Fields
复制标题
任意域上简化阿尔伯特代数的嵌入定理
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Holger P. Petersson
中科院分区：
文献类型：
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作者：
Holger P. Petersson
将Albert和Jacobson的两个经典嵌入定理以及Jacobson关于Albert（exceptional simple Jordan）代数在特征不为2的域上的嵌入定理推广到任意特征的基域上，证明了约化Albert代数的任意元素都可以嵌入到一个约化的3次9维绝对单子代数中，如果Albert代数从开始就被分裂，那么这个约化的3次9维绝对单子代数就可以被分裂.
Extending two classical embedding theorems of Albert and Jacobson and Jacobson for Albert (exceptional simple Jordan) algebra over fields of characteristic not two to base fields of arbitrary characteristic, we show that any element of a reduced Albert algebra can be embedded into a reduced absolutely simple subalgebra of degree 3 and dimension 9 which may be chosen to be split if the Albert algebra was split to begin with.