Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Extension Algebras and Quaternion Algebras Over Fields (of
  Characteristic not 2)   The paper presents a classification of quadratic extension algebras, also
known as algebras of degree 2, as well as several characterizations of
quaternion algebras over a field (of characteristic not 2). The presentation is
not restricted to finite-dimensional algebras. The 'pure calculus' on a
quaternion algebra is introduced; it generalizes the 'vector calculus' of the
Hamilton's quaternions, and is instrumental in establishing, in a clear and
simple way, the isomorphism between the group consisting of all automorphisms
and all anti-automorphisms of a quaternion algebra and the orthogonal group of
the norm form on the subspace of pure quaternions. The paper concludes with a
glimpse of quaternion algebras over an integral domain (of characteristic not
2), and of their facility in studying ternary quadratic forms over an integral
domain.

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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org