Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note about levels and sublevels of algebras obtained by the
  Cayley-Dickson process   In this paper, \thinspace \thinspace we generalize the concepts of \thinspace
level \thinspace and \thinspace sublevel of a composition algebra to algebras
obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for
every}$t\in \Bbb{N},${\small % \ a division algebra}$A_{t}${\small \ of
dimension}$2^{t}${\small \ over the power-series
field}$K\{X_{1},X_{2},...,X_{t}\}.\,${\small \ This gives us the possibility to
construct a division algebra of \thinspace dimension \thinspace
2}$^{t}\,${\small and prescribed \thinspace level and sublevel \thinspace
\thinspace 2}$^{k}${\small ,\thinspace \thinspace}$k,\,t\in \Bbb{%
N}^{*}${\small \ and a division algebra of \thinspace dimension \thinspace}$%
2^{t}+1,t\in \Bbb{N}\,${\small and prescribed \thinspace level and sublevel}%
$\,2^{k}+1,k\in \Bbb{N}.\,\medskip $

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga