Equivariant injectivity of crossed products

Abstract: We introduce the notion of a G-operator space, which consists of an action of a locally compact quantum group G on an operator space X, and we study the notion of G-equivariant injectivity for such an operator space. We define a natural associated crossed product operator space X ⋊ G, on which both the locally compact quantum group G and its dual act. We completely characterise when these crossed products are equivariantly injective with respect to these actions. We discuss how these results generalise and unify several recent results from the literature and we give some new applications.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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