Convergence of Peter-Weyl Truncations of Compact Quantum Groups

Abstract: A fundamental principle of noncommutative geometry is to encode geometric information by spectral data, formalised in the notion of spectral triples. In physical practice there are, however, always obstructions on the availability of such data, and one might be led to considering truncated versions of spectral triples instead. In this talk we will take a closer look at this formalism and explore it within the framework of compact quantum metric spaces. In particular we will consider compact quantum groups as compact quantum metric spaces when equipped with an invariant lip-norm. We will discuss complete Gromov-Hausdorff convergence of truncations arising from the Peter-Weyl decomposition of a compact quantum group.

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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