現代数学の系譜11 ガロア理論を読む8at MATH
現代数学の系譜11 ガロア理論を読む8 - 暇つぶし2ch426:現代数学の系譜11 ガロア理論を読む
14/04/05 20:16:57.56
>>425
補足
Octonion=8元数
これが結構応用があるという
URLリンク(en.wikipedia.org)
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O.
There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H.
The octonions are the largest such algebra, with eight dimensions, double the number of the quaternions from which they are an extension.
They are noncommutative and nonassociative, but satisfy a weaker form of associativity, namely they are alternative.

Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used.
Despite this, they have some interesting properties and are related to a number of exceptional structures in mathematics, among them the exceptional Lie groups.
Additionally, octonions have applications in fields such as string theory, special relativity, and quantum logic.

The octonions were invented in 1843 by John T. Graves, inspired by his friend William Hamilton's discovery of quaternions. Graves called his discovery octaves.
They were discovered independently by Arthur Cayley[1] and are sometimes referred to as Cayley numbers or the Cayley algebra.


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