具有部分对易关系的量子群
Quantum groups with partial commutation relations
摘要：
我们定义了新的非对易球的部分交换关系的坐标。我们研究了最大地作用于它们的量子群，这产生了新的量子版本的正交群：它们是部分交换的方式，使它们不插入之间的经典和自由量子版本的正交群。同样，我们定义非内插，部分交换量子版本的对称群恢复比雄的量子自同构群的图形。它们符合Speicher和Wysoczanski最近定义的经典独立性和自由独立性的混合（重新发现Mlotkowski的$Λ$ -freeness），这是由于de Finetti定理的某些弱化版本。
英文摘要：
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 $Λ$-freeness of Mlotkowski), due to some weakened version of a de Finetti theorem.
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