A HIGHER CATEGORY APPROACH TO TWISTED ACTIONS ON C*-ALGEBRAS

作者：Buss Alcides^*; Meyer Ralf; Zhu Chenchang

来源：Proceedings of the Edinburgh Mathematical Society, 2013, 56(2): 387-426.

DOI：10.1017/S0013091512000259

• Green twisted action
• Busby-Smith twisted action
• Fell bundle
• 2-category
• Morita equivalence
• Packer-Raeburn Stabilization Trick

C*-algebras form a 2-category with *-homomorphisms or correspondences as morphisms and unitary intertwiners as 2-morphisms. We use this structure to define weak actions of 2-categories, weakly equivariant maps between weak actions and modifications between weakly equivariant maps. In the group case, we identify the resulting notions with known ones, including Busby-Smith twisted actions and the equivalence of such actions, covariant representations and saturated Fell bundles. For 2-groups, weak actions combine twists in the sense of Green, and Busby and Smith.
The Packer-Raeburn Stabilization Trick implies that all Busby-Smith twisted group actions of locally compact groups are Morita equivalent to classical group actions. We generalize this to actions of strict 2-groupoids.

• 出版日期2013-6