Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum groups with partial commutation relations   We define new noncommutative spheres with partial commutation relations for
the coordinates. We investigate the quantum groups acting maximally on them,
which yields new quantum versions of the orthogonal group: They are partially
commutative in a way such that they do not interpolate between the classical
and the free quantum versions of the orthogonal group. Likewise we define
non-interpolating, partially commutative quantum versions of the symmetric
group recovering Bichon's quantum automorphism groups of graphs. They fit with
the mixture of classical and free independence as recently defined by Speicher
and Wysoczanski (rediscovering $\Lambda$-freeness of Mlotkowski), due to some
weakened version of a de Finetti theorem.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin