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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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147862 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147862 |
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irk-123456789-1478622019-02-17T01:23:17Z Fixed Point Algebras for Easy Quantum Groups Gabriel, O. Weber, M. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147862 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Gabriel, O. Weber, M. |
| spellingShingle |
Gabriel, O. Weber, M. Fixed Point Algebras for Easy Quantum Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gabriel, O. Weber, M. |
| author_sort |
Gabriel, O. |
| title |
Fixed Point Algebras for Easy Quantum Groups |
| title_short |
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_sort |
fixed point algebras for easy quantum groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147862 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT gabrielo fixedpointalgebrasforeasyquantumgroups AT weberm fixedpointalgebrasforeasyquantumgroups |
| first_indexed |
2023-05-20T17:28:42Z |
| last_indexed |
2023-05-20T17:28:42Z |
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1796153391424995328 |