R.B. Brown’s scientific contributions

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Publications (1)


On generalized Cayley-Dickson algebras
  • Article

March 1967

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38 Reads

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75 Citations

Pacific Journal of Mathematics

R.B. Brown

Among those algebras whose multiplication does not satisfy the associative law is a particular family of noncommutative Jordan algebras, the generalized Cayley-Dickson algebras. These are certain central simple algebras whose dimensions are all powers of two. Most of this paper is concerned with giving the classification up to isomorphism of those of dimensions 16, 32, and 64 and determining the automorphism groups. In addition to this some generalized Cayley-Dicksondivision algebras are constructed. Precise criteria for when the 16-dimensional algebras are division algebras are formulated and applied to algebras over some common fields. For higher dimensions no such criteria are given. However, specific examples of division algebras for each dimension 2t are constructed over power-series fields.

Citations (1)


... The product of two sedenions can be determined using the multiplication table in [1]. The involution of a sedenion element w is given by [50]. The automorphisms can be explicitly stated as follows; ...

Reference:

Modelling three fermion generations with S 3 family symmetry within ℂℓ(8)
On generalized Cayley-Dickson algebras
  • Citing Article
  • March 1967

Pacific Journal of Mathematics