A functorial approach to the C*-algebras of a graph

$C^*$-correspondence functoriality of Cuntz-Pimsner algebras

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. The objects in our domain category are $C^*$-correspondences, and the morphisms are the isomorphism classes of $C^*$-correspondences satisfying certain conditions. As an application, we recover a well-known result of Muhly and Solel. In fact, we show that functoriality leads us to a more generalized result: strongly Morita equivalent $C^*$-correspondences have Morita equivalent Cuntz-Pimsner algebras.

Functoriality of Cuntz-Pimsner correspondence maps

We show that the passage from a $C^\ast$-correspondence to its Cuntz-Pimsner $C^\ast$-algebra gives a functor on a category of $C^\ast$-correspondences with appropriately defined morphisms. Applications involving topological graph $C^\ast$-algebras are discussed, and an application to crossed-product correspondences is presented in detail.

Functoriality of group algebras acting on $L^p$-spaces

We continue our study of group algebras acting on $L^p$-spaces, particularly of algebras of $p$-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$-pseudofunctions are functorial with respect to homomorphisms that are either injective, or whose kernel is amenable and has finite index. We also show that the universal completion of the group algebra with respect to representations on $L^p$-spaces, is functorial with respect to quotient maps. As an application, we show that the algebras of $p$- and $q$-pseudofunctions on $\mathbb{…

图上移动的函子性与图代数的扩展协变函子性

The functoriality of moves on graphs and the extended covariant functoriality of graph algebras

本文通过引入图逆半群的正则同态作为态射，构造了图的新范畴，并建立了到C*-代数范畴的协变函子，扩展了已知的协变函子。

群胚与 Fell 丛 $C^*$-代数的函子性

Functoriality for groupoid and Fell bundle $C^*$-algebras

本文定义 étale 群胚及 Fell 丛的新态射，建立到 $C^*$-代数的函子，并刻画 Cartan 对、Weyl 群胚与扭曲间的范畴等价及余极限保持性。

Functoriality of Rieffel's Generalised Fixed-Point Algebras for Proper Actions

We consider two categories of C*-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C*-algebraic contexts. We show that Rieffel's construction of a fixed-point algebra for a proper action can be made into functors defined on these categories, and that his Morita equivalence then gives a natural isomorphism between these functors and crossed-product functors. These results have interesting applications to non-a…