Fixed points of compact quantum groups actions on Cuntz algebras
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Fixed points of compact quantum groups actions on Cuntz algebras. / Gabriel, Olivier.
In: Annales Henri Poincare, Vol. 15, No. 5, 2014, p. 1013-1036.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 155424798