Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An alternate Cayley-Dickson product   Although the Cayley-Dickson algebras are twisted group algebras, little
attention has been paid to the nature of the Cayley-Dickson twist. One reason
is that the twist appears to be highly chaotic and there are other interesting
things about the algebras to focus attention upon. However, if one uses a
doubling product for the algebras different from yet equivalent to the ones
commonly used and if one uses a numbering of the basis vectors different from
the standard basis a quite beautiful and highly periodic twist emerges. This
leads easily to a simple closed form formula for the product of any two basis
vectors of a Cayley-Dickson algebra.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol