Induced coactions along a homomorphism of locally compact quantum groups
Induced coactions along a homomorphism of locally compact quantum groups
复制标题
沿局部紧量子群同态的诱导相互作用
DOI：
10.1016/j.jfa.2022.109462
复制
发表时间：
2022
影响因子：
1.7
通讯作者：
Kitamura Kan
中科院分区：
文献类型：
--
作者：
Futamata Haon;Fukuda Masahiro;Umeda Rie;Yamashita Keitaro;Tomita Atsuhiro;Takahashi Satoe;Shikakura Takafumi;Hayashi Shigehiko;Kusakizako Tsukasa;Nishizawa Tomohiro;Homma Kazuaki;Nureki Osamu;Kitamura Kan
本文考虑C*-代数上沿着局部紧量子群的同态的诱导余作用，这些局部紧量子群不必给出闭量子子群。我们的方法推广了由Vaes构造的诱导余作用，也包括某些不动点代数。我们专注于当同态满足适当性的量子模拟的情况下。沿着这样一个同态的诱导余作用沿着仍然承认在闭量子子群的情况下已知的各种性质的自然公式，例如不相容性和带限制的伴随性。另外，我们还证明了诱导余作用与限制之间的关系，这种关系类似于代数上模的基变换公式。作为应用，我们给出了一个例子，证明了具有遗忘函子的几种1-范畴的相互作用不能恢复原来的量子群。
We consider induced coactions on C*-algebras along a homomorphism of locally compact quantum groups which need not give a closed quantum subgroup. Our approach generalizes the induced coactions constructed by Vaes, and also includes certain fixed point algebras. We focus on the case when the homomorphism satisfies a quantum analogue of properness. Induced coactions along such a homomorphism still admit the natural formulations of various properties known in the case of a closed quantum subgroup, such as imprimitivity and adjointness with restriction. Also, we show a relationship of induced coactions and restriction which is analogous to base change formula for modules over algebras. As an application, we give an example that shows several kinds of 1-categories of coactions with forgetful functors cannot recover the original quantum group.