Lattice of Idempotent States on a Locally Compact Quantum Group

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

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.

The Quantum Double of a (locally) Compact Group

We generalise the quantum double construction of Drinfel’d to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the ∗-algebra structure of the quantum double. If the conjugacy classes in the group are countably separated, then we classify the irreducible ∗-representations by using the connection with so–called transformation group...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Idempotent Measures on Compact Semigroups

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

On a Certain Invariant of a Locally Compact Group

Group here always means a locally compact Hausdorff group, subgroup means a closed subgroup. Let G be a group, H a subgroup and G/H the locally compact homogeneous space of left cosets x = xH. We denote by $(G) [®(G/H)] the family of all compact subsets of G [G/H], The group G acts on G/H in a natural way. If X C.G and Y QG/H, write XY for the set of all elements xy, x £ I , j £ Y. Now assume t...