Q-system completion for C⁎ 2-categories
Q-system completion for C⁎ 2-categories
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DOI：
10.1016/j.jfa.2022.109524
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发表时间：
2022-04
影响因子：
1.7
通讯作者：
Quanlin Chen;Roberto Hernández Palomares;Corey Jones;David Penneys
中科院分区：
文献类型：
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作者：
Quanlin Chen;Roberto Hernández Palomares;Corey Jones;David Penneys
C-Frobenius 2-范畴中的Q-系是可分⁎代数对象的酉型，可以看作是高次幂等元的酉型。我们定义了C-⁎2-范畴的一个高酉幂等完备性，称为Q-系完备化，并研究了它的性质。通过构造逆实现⁎-2-函子，证明了单位C-⁎-代数的右对应的C-†-2-范畴是Q-系统完备的。利用这一结果，我们构造了具有连通谱的连续迹C-⁎-代数上群论酉合范畴的诱导作用。
A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties. We show that the C⁎ 2-category of right correspondences of unital C⁎-algebras is Q-system complete by constructing an inverse realization†-2-functor. We use this result to construct induced actions of group theoretical unitary fusion categories on continuous trace C⁎-algebras with connected spectra.