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Classifiable C*-algebras have quantum symmetries
Kan Kitamura
We show that every classifiable simple C*-algebra, in particular the Jiang-Su algebra, admits outer actions of several discrete quantum groups, such as finite quantum groups and du…
Actions of tensor categories on Kirchberg algebras
Kan Kitamura
We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unit…
A note on quantum subgroups of free quantum groups
Mao Hoshino, Kan Kitamura
In this short note, quantum subgroups in finite free products of the Pontryagin duals of free unitary quantum groups are classified. They correspond to pairs of a subgroup and…
Tensor category equivariant KK-theory
Yuki Arano, Kan Kitamura, Yosuke Kubota
In this paper, we introduce Kasparov's bivariant K-theory that is equivariant under symmetries of a C*-tensor category. It is motivated by some dualities in quantum group equivaria…
Partial Pontryagin duality for actions of quantum groups on C*-algebras
Kan Kitamura
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…