Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Subalgebra Structure of the Cayley-Dickson Algebra of Dimension 32
  (trigintaduonion)   The Cayley-Dickson algebras R (real numbers), C (complex numbers), H
(quaternions), O (octonions), S (sedenions), and T (trigintaduonions) have
attracted the attention of several mathematicians and physicists because of
their important applications in both pure mathematics and theoretical physics.
This paper deals with the determination of the subalgebra structure of the
algebra T by analyzing the loop T_L of order 64 generated by its 32 basis
elements. The analysis shows that T_L is a non-associative finite invertible
loop (NAFIL) with 373 non-trivial subloops of orders 32, 16, 8, 4, and 2 all of
which are normal. These subloops generate subalgebras of T of dimensions 16, 8,
4, 2, and 1 which form the elements of its structure.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat