Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Product of three octonions   This paper is devoted to octonions that are the eight-dimensional
hypercomplex numbers characterized by multiplicative non-associativity. The
decomposition of the product of three octonions with the conjugated central
factor into the sum of mutually orthogonal anticommutator, commutator and
associator, is introduced in an obvious way by commuting of factors and
alternating the multiplication order. The commutator is regarded as a
generalization of the cross product to the case of three arguments both for
quaternions and for octonions. It is verified that the resulting additive
decomposition is equivalent to the known solution derived and presented by S.
Okubo in a cumbersome form.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th