Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Octonion-like Associative Division Algebra   Using elementary linear algebra, this paper clarifies and proves some
concepts about a recently introduced octonion-like associative division algebra
over R. This octonion-like algebra is actually the same as the
split-biquaternion algebra, an even subalgebra of Clifford algebra Cl4,0(R) ,
which is isomorphic to Cl0,3(R) . For two seminorms described in the paper, it
is shown that the octonion-like algebra is a seminormed composition algebra
over R. Moreover, additional results related to the computation of inverse
numbers in the octonion-like algebra are introduced, showing that the
octonion-like algebra is a seminormed division algebra over R, i.e., division
by any number is possible as long as the two seminorms are non-zero. Additional
results on normalization of octonion-like numbers and some involutions are also
presented. The elementary linear algebra descriptions used in the paper also
allow straightforward software implementations of the octonion-like algebra.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom