Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalizers and permutative endomorphisms of the $2$-adic ring
  $C^*$-algebra   A complete description is provided for the unitary normalizer of the diagonal
Cartan subalgebra $\mathcal{D}_2$ in the $2$-adic ring $C^*$-algebra
$\mathcal{Q}_2$, which generalizes and unifies analogous results for Cuntz and
Bunce-Deddens algebras. Furthermore, the inclusion
$\mathcal{O}_2\subset\mathcal{Q}_2$ is proved not to be regular. Finally,
countably many novel permutative endomorphisms of $\mathcal{Q}_2$ are exhibited
with prescribed images of the generator $U$.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an