八元数子代数

Pub Date : 2024-10-11 DOI:10.1016/j.jalgebra.2024.10.004
Norbert Knarr, Markus J. Stroppel
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引用次数: 0

摘要

对于任意的单元八元数代数,我们可以确定所有的子代数。结果发现,维数小于四的每个子代数都是联立的,而维数大于四的每个子代数都不是联立的。在任何分裂八元数代数中,都存在维数为四的联立子代数和非联立子代数。除了幂等子所跨的一维子代数外,任何两个同构的子代数在自动变形下都在同一轨道上。
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Subalgebras of octonion algebras
For an arbitrary unitary octonion algebra, we determine all subalgebras. It turns out that every subalgebra of dimension less than four is associative, while every subalgebra of dimension greater than four is not associative. In any split octonion algebra, there are both associative and non-associative subalgebras of dimension four. Except for one-dimensional subalgebras spanned by idempotents, any two isomorphic subalgebras are in the same orbit under automorphisms.
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