C*-代数扭张量积的量子对称性
Quantum symmetries of the twisted tensor products of C*-algebras
AI总结：
本文研究带正交滤过的C*-代数扭张量积的量子对称群，证明满足扭形式假设时该群为原滤过量子对称群的广义Drinfeld double，给出离散群交叉积的应用及主定理不成立的反例。
摘要：
我们研究了带有正交滤过的C*-代数范畴中扭张量积的构造，并在关于扭形式的特定假设下，计算了相应的量子对称群，结果表明该群是原滤过的量子对称群的广义Drinfeld double。我们展示了这些结果如何应用于一大类由离散群作用产生的C*-代数交叉积。我们还讨论了一个不满足我们主定理假设、且量子对称群不是广义Drinfeld double的例子。
英文摘要：
We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns out to be the generalised Drinfeld double of the quantum symmetry groups of the original filtrations. We show how these results apply to a wide class of crossed products of C*-algebras by actions of discrete groups. We also discuss an example where the hypothesis of our main theorem is not satisfied and the quantum symmetry group is not a generalised Drinfeld double.
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