K-theory of locally compact modules over orders

Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Multipliers of locally compact quantum groups via Hilbert C*-modules

A result of Gilbert shows that every completely bounded multiplier f of the Fourier algebra A(G) arises from a pair of bounded continuous maps α, β : G → K, where K is a Hilbert space, and f(s−1t) = (β(t)|α(s)) for all s, t ∈ G. We recast this in terms of adjointable operators acting between certain Hilbert C∗-modules, and show that an analogous construction works for completely bounded left mu...

Uniform continuity over locally compact quantum groups

We define, for a locally compact quantum group G in the sense of Kustermans– Vaes, the space of LUC (G) of left uniformly continuous elements in L∞(G). This definition covers both the usual left uniformly continuous functions on a locally compact group and Granirer’s uniformly continuous functionals on the Fourier algebra. We show that LUC (G) is an operator system containing the C∗-algebra C0(...

P-Amenable Locally Compact Hypergroups

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any OE-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] ∼= ⊕χMχ is explicitly computable and each Mχ is in fact a matrix ring over a field, this leads to an algorithm that eithe...