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  • Octonion - Wikipedia
    Octonions have applications in fields such as string theory, special relativity and quantum logic The Cayley–Dickson construction builds the octonions from the quaternions and in turn builds the sedenions from the octonions
  • Octonions - Department of Mathematics
    Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups We also touch upon their applications in quantum logic, special relativity and supersymmetry Table of Contents:
  • What lies beyond the Sedenions - Mathematics Stack Exchange
    Remark: I am left wondering what is gained by going past Octonions The the first 4 are very special as they are the unique 4 normed divison algebras over $\mathbb {R}$ Perhaps someone with more knowledge can point out the possible uses of the Sedenions and their higher counterparts
  • List of numbers - Googology Wiki
    This is a list of googolisms in ascending order This list contains ill-defined large numbers, e g BEAF numbers beyond tetrational arrays, BIG FOOT, Little Bigeddon
  • Octonion -- from Wolfram MathWorld
    A typical octonion is of the form a+bi_0+ci_1+di_2+ei_3+fi_4+gi_5+hi_6, where each of the triples (i_0,i_1,i_3), (i_1,i_2,i_4), (i_2,i_3,i_5), (i_3,i_4,i_6), (i_4,i_5,i_0), (i_5,i_6,i_1), (i_6,i_0,i_2) behaves like the quaternions (i,j,k) Octonions are not associative
  • Octonions and sedenions - Iowa State University
    After that, it continues to produce algebras satisfying both distributive laws, but the Euclidean norms are no longer multiplicative, and indeed the algebras start to have zero-divisors
  • Hypercomplex Numbers: Quaternion, Octonion, Sedenian, and beyond - Yak
    Cayley-Dickson Construction First, we define the reals R where a ∈ R implies that a* = a Given an algebra A of diminsion n, we create, using the Cayley-Dickson construction, an algebra of dimension 2n by taking pairs (a, b) ∈ A × A and thus define the standard operations:
  • Maths - Octonion - Martin Baker - EuclideanSpace
    Octonions are represented by 8 numbers (1 real and 7 imaginary) We might expect this sequence to continue with an element consisting of 16 numbers, but such an algebra does not exist, and the sequence ends with octonions
  • book:go2:octonionsn - Geometry of the Octonions
    What is the result of conjugating an octonion by $\ell$? First of all, there are no associativity issues here since there are only two octonions involved, namely $\ell$ and $x$
  • What group is next after octillion? - Answers
    The power of one thousand (or one million, depending on whether you are using the short-scale American version of the system or the long-scale English and continental European usage of the system)





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