arXiv Analytics

Sign in

arXiv:0906.2362 [math.OA]AbstractReferencesReviewsResources

A New Characterisation of Idempotent States on Finite and Compact Quantum Groups

Uwe Franz, Adam Skalski

Published 2009-06-12Version 1

We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idempotent states on a finite quantum group and by its coidalgebras are isomorphic. We show furthermore that these lattices are also isomorphic for compact quantum groups, if one restricts to expected coidalgebras.

Comments: 9 pages
Journal: Comptes Rendus Mathematique Vol. 347, pp. 991-996, 2009
Categories: math.OA, math.QA
Subjects: 17B37, 43A05, 46L65
Related articles: Most relevant | Search more
arXiv:0903.2363 [math.OA] (Published 2009-03-13, updated 2011-02-08)
Idempotent states on compact quantum groups and their classification on U_q(2), SU_q(2), and SO_q(3)
arXiv:1012.2004 [math.OA] (Published 2010-12-09, updated 2011-12-21)
On Square Roots of the Haar State on Compact Quantum Groups
arXiv:1102.2051 [math.OA] (Published 2011-02-10, updated 2011-07-05)
Idempotent states on locally compact quantum groups

Links

Toolbox