Partial Pontryagin duality for actions of quantum groups on C*-algebras
Partial Pontryagin duality for actions of quantum groups on C*-algebras
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发表时间：
2022-10
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通讯作者：
Kan Kitamura
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作者：
Kan Kitamura
本文比较了局部紧量子群的两种构造：双交叉积和双交叉积在C*-代数上的作用。作为Baaj-Skandalis对偶的推广，我们给出了它们之间的对偶。在量子双打的情况下，这种对偶性也保持了由扭曲张量积给出的幺半群结构。我们还讨论了它的后果等变卡斯帕罗夫理论的量子类似的鲍姆-康纳斯猜想。
We compare actions on C*-algebras of two constructions of locally compact quantum groups, the bicrossed product and the double crossed product. We give a duality between them as a generalization of Baaj-Skandalis duality. In the case of quantum doubles, this duality also preserves monoidal structures given by twisted tensor products. We also discuss its consequences for equivariant Kasparov theories in relation to the quantum analogue of the Baum-Connes conjecture.