论文标题
Riesz在紧凑型量子组和牢固性上转变
Riesz transforms on compact quantum groups and strong solidity
论文作者
论文摘要
本文的主要目的之一是给出大量坚固的紧凑型量子基团。我们通过使用量子马尔可夫半组（QMS）和非交通riesz的变换来做到这一点。我们在紧凑型量子组上引入了中央乘数的QMS属性，我们将其称为几乎通勤的互穿的近似线性。我们表明，在免费产品，单体等效性，免费花圈产品和双量子亚组下，该特性是稳定的。示例特别包括所有（较高维度）的免费正交容易量子组。 然后，我们表明，具有QM的紧凑型量子组几乎是线性的，几乎与交通工具相互交织，满足了立即梯度 - $ \ MATHCAL {S} _2 $来自[Cas21]的条件，并得出强固体结果（遵循[Cas21]，[ozpo10]，[ozpo10]，[pet09]）。使用非交通性的Riesz变换，我们还表明这些量子组具有Akemann-Ostrand属性。特别是再次遵循相同的强固定结果（现在遵循[ISO15B]，[POVA14]）。
One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semi-groups (QMS's) and non-commutative Riesz transforms. We introduce a property for QMS's of central multipliers on a compact quantum group which we shall call approximate linearity with almost commuting intertwiners. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a QMS that is approximately linear with almost commuting intertwiners, satisfies the immediately gradient-$\mathcal{S}_2$ condition from [Cas21] and derive strong solidity results (following [Cas21], [OzPo10], [Pet09]). Using the non-commutative Riesz transform we also show that these quantum groups have the Akemann-Ostrand property; in particular the same strong solidity results follow again (now following [Iso15b], [PoVa14]).
