Actions of compact and discrete quantum groups on operator systems

Abstract: We introduce the notion of an action of a discrete or compact quantum group on an operator system, and study equivariant operator system injectivity. Given an action of a discrete quantum group on an operator system X, we introduce associated crossed products, and we prove that equivariant injectivity of the operator system X is equivalent with dual equivariant injectivity of the associated crossed products. As an application of this result, we prove a duality result for equivariant injective envelopes. This is joint work with Lucas Hataishi.

category theoryoperator 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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