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QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS

Part of: Groups and algebras in quantum theory Selfadjoint operator algebras Linear algebraic groups and related topics Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  27 September 2019

PAWEŁ JÓZIAK Open the ORCID record for PAWEŁ JÓZIAK [Opens in a new window]
PAWEŁ JÓZIAK*
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland e-mail: [email protected]
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Abstract

We answer a question of Skalski and Sołan (2016) about inner faithfulness of the Curran’s map of extending a quantum increasing sequence to a quantum permutation. Roughly speaking, we find a inductive setting in which the inner faithfulness of Curran’s map can be boiled down to inner faithfulness of similar map for smaller algebras and then rely on inductive generation result for quantum permutation groups of Brannan, Chirvasitu and Freslon (2018).

MSC classification

Primary: 46L89: Other “noncommutative” mathematics based on $C^*$-algebra theory 20G42: Quantum groups (quantized function algebras) and their representations
Secondary: 81R50: Quantum groups and related algebraic methods 16T20: Ring-theoretic aspects of quantum groups
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 631 - 639
Copyright
© Glasgow Mathematical Journal Trust 2019

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