Fixed Point Algebras for Easy Quantum Groups
Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author, we prove tha...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147862 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Fixed Point Algebras for Easy Quantum Groups / O. Gabriel, M. Weber // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 44 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862625200172957696 |
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| author | Gabriel, O. Weber, M. |
| author_facet | Gabriel, O. Weber, M. |
| citation_txt | Fixed Point Algebras for Easy Quantum Groups / O. Gabriel, M. Weber // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 44 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the K-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group Sn⁺, the free orthogonal quantum group On⁺ and the quantum reflection groups Hns⁺. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups, which are related to Hopf-Galois extensions.
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| first_indexed | 2025-12-07T13:34:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147862 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:34:00Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gabriel, O. Weber, M. 2019-02-16T09:32:04Z 2019-02-16T09:32:04Z 2016 Fixed Point Algebras for Easy Quantum Groups / O. Gabriel, M. Weber // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 44 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L80; 19K99; 81R50 DOI:10.3842/SIGMA.2016.097 https://nasplib.isofts.kiev.ua/handle/123456789/147862 Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the K-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group Sn⁺, the free orthogonal quantum group On⁺ and the quantum reflection groups Hns⁺. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups, which are related to Hopf-Galois extensions. The second author was partially funded by the ERC Advanced Grant on Non-Commutative
 Distributions in Free Probability, held by Roland Speicher, Saarland University. The first author
 was supported by the Danish National Research Foundation through the Centre for Symmetry
 and Deformation (DNRF92) and by the Engineering and Physical Sciences Research Council
 Grant EP/L013916/1, since the first results of this work were obtained during the first author’s
 postdoc in Glasgow.
 Both authors are grateful to Roland Speicher’s ERC Advanced Grant and Christian Voigt
 for enabling their respective stays in Scotland where this collaboration started. They also thank
 the anonymous referees for their thourough reviews and remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fixed Point Algebras for Easy Quantum Groups Article published earlier |
| spellingShingle | Fixed Point Algebras for Easy Quantum Groups Gabriel, O. Weber, M. |
| title | Fixed Point Algebras for Easy Quantum Groups |
| title_full | Fixed Point Algebras for Easy Quantum Groups |
| title_fullStr | Fixed Point Algebras for Easy Quantum Groups |
| title_full_unstemmed | Fixed Point Algebras for Easy Quantum Groups |
| title_short | Fixed Point Algebras for Easy Quantum Groups |
| title_sort | fixed point algebras for easy quantum groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147862 |
| work_keys_str_mv | AT gabrielo fixedpointalgebrasforeasyquantumgroups AT weberm fixedpointalgebrasforeasyquantumgroups |