Fixed point algebras for easy quantum groups

TY - JOUR

T1 - Fixed point algebras for easy quantum groups

AU - Gabriel, Olivier

AU - Weber, Moritz

PY - 2016

Y1 - 2016

N2 - 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 S+ n,the free orthogonal quantum group O+ n and the quantum reflection groups Hs+ n. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions.

AB - 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 S+ n,the free orthogonal quantum group O+ n and the quantum reflection groups Hs+ n. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions.

KW - Easy quantum groups

KW - Free actions

KW - Free orthogonal quantum groups

KW - Fusion rules

KW - K-theory

KW - Kirchberg algebras

KW - Noncrossing partitions

KW - Quantum permutation groups

KW - Quantum reflection groups

UR - http://www.scopus.com/inward/record.url?scp=84996555070&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2016.097

DO - 10.3842/SIGMA.2016.097

M3 - Journal article

AN - SCOPUS:84996555070

SN - 1815-0659

VL - 12

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 097

ER -