Levy–Khintchine decomposition for convolution semigroups of states

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• Martin Lindsay (Lancaster University)
• Wednesday 04 December 2024, 11:10-11:50
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

Given a convolution semigroup of states on a compact quantum group, can its generating functional be expressed as the sum of a `gaussian’ generating functional and a `wholly non-gaussian’ one – in short, does it have a Levy-Khintchine type decomposition? A key new tool for addressing this question is the notion of approximate innerness for derivations on the Hopf -algebra of the quantum group with respect to a -algebra representation and the counit. A satisfactory, and positive, answer is found in the case of certain classes of q-deformed compact Lie groups. The talk is based on joint work with Uwe Franz, Anna Kula and Michael Skeide.

This talk is part of the Isaac Newton Institute Seminar Series series.

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