The planar algebra of a coaction - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Journal of Operator Theory Année : 2005

The planar algebra of a coaction

Résumé

We study actions of ``compact quantum groups\'\' on ``finite quantum spaces\'\'. According to Woronowicz and to general $\\c^*$-algebra philosophy these correspond to certain coactions $v:A\\to A\\otimes H$. Here $A$ is a finite dimensional $\\c^*$-algebra, and $H$ is a certain special type of Hopf *-algebra. If $v$ preserves a positive linear form $\\phi :A\\to\\c$, a version of Jones\' ``basic construction\'\' applies. This produces a certain $\\c^*$-algebra structure on $A^{\\otimes n}$, plus a coaction $v_n :A^{\\otimes n}\\to A^{\\otimes n}\\otimes H$, for every $n$. The elements $x$ satisfying $v_n(x)=x\\otimes 1$ are called fixed points of $v_n$. They form a $\\c^*$-algebra $Q_n(v)$. We prove that under suitable assumptions on $v$ the graded union of the algebras $Q_n(v)$ is a spherical $\\c^*$-planar algebra.

Dates et versions

hal-00012808 , version 1 (27-10-2005)

Identifiants

Citer

Teodor Banica. The planar algebra of a coaction. Journal of Operator Theory, 2005, 53, pp.119-158. ⟨hal-00012808⟩
55 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More