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April 2021 Homogeneous quantum groups and their easiness level
Teo Banica
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Kyoto J. Math. 61(1): 171-205 (April 2021). DOI: 10.1215/21562261-2019-0077

Abstract

Given a closed subgroup GUN+ which is homogeneous, in the sense that we have SNGUN+, the corresponding Tannakian category C must satisfy span(NC2)Cspan(P). Based on this observation, we construct a certain integer pN{}, that we call the easiness level of G. The value p=1 corresponds to the case where G is easy, and we explore here, with some theory and examples, the case p>1. As a main application, we show that SNSN+ and other liberation inclusions, known to be maximal in the easy setting, remain maximal at the easiness level p=2 as well.

Acknowledgments

I would like to thank J. Bichon, B. Collins, and S. Curran for many discussions on maximality questions over the last few years. Thanks also go to Poulette.

Citation

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Teo Banica. "Homogeneous quantum groups and their easiness level." Kyoto J. Math. 61 (1) 171 - 205, April 2021. https://doi.org/10.1215/21562261-2019-0077

Information

Received: 17 June 2018; Revised: 6 March 2019; Accepted: 6 March 2019; Published: April 2021
First available in Project Euclid: 11 November 2020

Digital Object Identifier: 10.1215/21562261-2019-0077

Subjects:
Primary: 46L65
Secondary: 46L54

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 1 • April 2021
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