The Group Ring of a Locally Compact Group: I

The study of relation between existence of admissible vectors and amenability and compactness of a locally compact group

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

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...

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...

An example of a braided locally compact group

The notions of the crossed product and the braided category are discussed within the theory of C∗-algebras. Like in the purely algebraic approach of S. Majid these notions are used to generalize the quantum group theory. We give an example of a braided group. It coincides with the closed subset C = {z : |z| = . . . , q−2, q−1, 1, q, q2, . . . , 0} of the complex plane equipped with the q2braidi...

A Note on Semi-groups in a Locally Compact Group