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arXiv · 1110.2572

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

Erik Darpö·Ernst Dieterich
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Abstract

For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by a non-zero element are shown to form an invariant of A, called its double sign. The double sign causes the category of all real division algebras of a fixed dimension n>1 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 the category of all finite-dimensional real division algebras.

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Erik Darpö, Ernst Dieterich. 2011-10-12. The double sign of a real division algebra of finite dimension greater than one. https://arxiv.org/abs/1110.2572

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