TY - JOUR

T1 - Fixed points of compact quantum groups actions on Cuntz algebras

AU - Gabriel, Olivier

PY - 2014

Y1 - 2014

N2 - Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C *-algebra, compute its K-theory and prove a “stability property”: the fixed points only depend on the CQG via its fusion rules. We apply the theory to SU_q(N) and illustrate by explicit computations for SU_q(2) and SU_q(3). This construction provides examples of free actions of CQG (or “principal noncommutative bundles”).

AB - Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C *-algebra, compute its K-theory and prove a “stability property”: the fixed points only depend on the CQG via its fusion rules. We apply the theory to SU_q(N) and illustrate by explicit computations for SU_q(2) and SU_q(3). This construction provides examples of free actions of CQG (or “principal noncommutative bundles”).

KW - Faculty of Science

KW - K-theory

KW - purely infinite C-algebra

KW - Kirchberg algebra

KW - compact quantum group

KW - fusion rules

KW - free actions

KW - crossed products

U2 - 10.1007/s00023-013-0265-5

DO - 10.1007/s00023-013-0265-5

M3 - Journal article

VL - 15

SP - 1013

EP - 1036

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -