Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right)$ as a
  symmetry of division algebraic ladder operators   We demonstrate a model which captures certain attractive features of $SU(5)$
theory, while providing a possible escape from proton decay. In this paper we
show how ladder operators arise from the division algebras $\mathbb{R}$,
$\mathbb{C}$, $\mathbb{H}$, and $\mathbb{O}$. From the $SU(n)$ symmetry of
these ladder operators, we then demonstrate a model which has much structural
similarity to Georgi and Glashow's $SU(5)$ grand unified theory. However, in
this case, the transitions leading to proton decay are expected to be blocked,
given that they coincide with presumably forbidden transformations which would
incorrectly mix distinct algebraic actions. As a result, we find that we are
left with $G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb{Z}_6$.
Finally, we point out that if $U(n)$ ladder symmetries are used in place of
$SU(n)$, it may then be possible to find this same $G_{sm}=SU(3)_C\times
SU(2)_L\times U(1)_Y / \mathbb{Z}_6$, together with an extra $U(1)_X$ symmetry,
related to $B-L$.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org