Crossed products of C∗-correspondences by amenable group actions

Equivariant -correspondences and compact quantum group actions on Pimsner algebras

“…To end this Introduction, let us mention that when a first draft of the present article was being written, the preprint [Kim14] was brought to our notice. The author proves a similar result to that of ours but goes on to another direction, along the lines of [HN08,KQR15]. In particular, the author considers coactions of not-necessarilyunital Hopf C * -algebras on Pimsner algebras and identifies the crossed product as the Pimsner algebra of the crossed product C * -correspondence.…”

Group Actions on Product Systems

“…Next, we introduce the concept of an action of a (locally compact and Hausdorff) group on a product system and then define the associated crossed product product system. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also row-finite and faithful, and, furthermore, we establish a version of the Hao-Ng Theorem (see Theorem 2.10 in [9]) for product systems over N k .…”

“…Given a locally compact group G and a C * -correspondence X over A, an action of G on X (see [9]) is a pair (α, β) with the following properties:…”

“…The crossed product X ⋊ β G of X by G is defined in [9] as the completion of the C c (G, A)-bimodule C c (G, X), and its (A ⋊ α G)-correspondence structure is uniquely determined by the following operations:…”