Generating Functionals for Locally Compact Quantum Groups

Adam Skalski, Ami Viselter

Research output: Contribution to journalArticlepeer-review

Abstract

Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital ∗-subalgebra with core-like properties in its domain. On the other hand we prove that every normalised, symmetric, hermitian conditionally positive functional on a dense ∗-subalgebra of the unitisation of the universal C$^∗$-algebra of a locally compact quantum group, satisfying certain technical conditions, extends in a canonical way to a generating functional. Some consequences of these results are outlined, notably those related to constructing cocycles out of convolution semigroups.

Original languageEnglish
Pages (from-to)10981-11009
Number of pages29
JournalInternational Mathematics Research Notices
Volume2021
Issue number14
DOIs
StatePublished - 1 Jul 2021

Bibliographical note

Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

ASJC Scopus subject areas

  • General Mathematics

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