Gaussian states and Gaussian parts of compact quantum groups

Abstract: I will motivate and explain the notion of a Gaussian state on a compact quantum group G, as introduced by Michael Schürmann. This concept leads to the idea of the Gaussian part of G, understood as the smallest quantum subgroup of G which supports all the Gaussian states of G. I will discuss properties of Gaussian states and compute Gaussian parts for several examples. This turns out to be related to quantum connectedness and certain topological generation questions for quantum subgroups. The talk will be based on joint work with Uwe Franz and Amaury Freslon.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This 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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