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Fixed Point Algebras for Easy Quantum Groups
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Fixed Point Algebras for Easy Quantum Groups
Інший ID:
2010 Mathematics Subject Classification: 46L80; 19K99; 81R50
DOI:10.3842/SIGMA.2016.097
DOI:10.3842/SIGMA.2016.097
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
631
Завантажень:
271
Анотація:
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.
