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 semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups 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 quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative 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 [27]).

这篇论文的主要目的之一是给出一大类强固紧量子群。我们通过使用量子马尔可夫半群和非交换 Riesz 变换来做到这一点。我们为紧量子群上的中心乘数的量子马尔可夫半群引入了一个性质，我们将其称为“具有几乎通勤缠绕体的近似线性”。我们表明该性质在自由乘积、幺半群等价、自由环状乘积和双量子子群下是稳定的。例子特别包括所有（高维）自由正交易量子群。

然后，我们证明具有量子马尔可夫半群的紧量子群与几乎互换的缠绕体近似线性满足来自 [10] 的立即梯度 - ${\mathcal {S}}_2$ 条件并得出强稳固性结果（遵循 [10 ]). 使用非交换 Riesz 变换，我们还表明这些量子群具有 Akemann–Ostrand 性质；特别是，同样强大的可靠性结果再次出现（现在在 [27] 之后）。