High Quality Content by WIKIPEDIA articles! In mathematics, the octonions are a nonassociative and noncommutative extension of the quaternions. Their 8-dimensional normed division algebra over the real numbers is the widest possible that can be obtained from the Cayley-Dickson construction. Possibly because they don't offer an associative multiplication, the octonions receive less attention than the quaternions. Despite this lack of popularity, they 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.

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