The double sign of a real division algebra of finite dimension greater than one

  title={The double sign of a real division algebra of finite dimension greater than one},
  author={Erik Darp{\"o} and Ernst-Wolfgang Dieterich},
For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A\{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category Dn of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of… CONTINUE READING

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