Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic quantum permutation groups   We discuss some algebraic aspects of quantum permutation groups, working over
arbitrary fields. If $K$ is any characteristic zero field, we show that there
exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra
$K^n$: this is a refinement of Wang's universality theorem for the (compact)
quantum permutation group. We also prove a structural result for Hopf algebras
having a non-ergodic coaction on the diagonal algebra $K^n$, on which we
determine the possible group gradings when $K$ is algebraically closed and has
characteristic zero.

10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga