C∗-completions and the DFR-algebra

Completions in Algebra and Topology

Completions of C-surfaces

Following an approach of Dolgachev, Pinkham and Demazure, we classified in [FlZa1] normal affine surfaces with hyperbolic C ∗-actions in terms of pairs of Q-divisors (D+, D−) on a smooth affine curve. In the present paper we show how to obtain from this description a natural equivariant completion of these C∗-surfaces. Using elementary transformations we deduce also natural completions for whic...

Completions of Partially Ordered Sets and Universal Algebra

The results' in this paper were motivated by a search for the answers to the following questions : When can a given partially ordered algebra be embedded in a complete partially ordered algebra in such a fashion that the original algebra is dense and that the operations acquire or maintain continuity properties? What type of identities are preserved under such embeddings? Properties of extensio...

Generalised Hecke Algebras and C * -completions

For a Hecke pair (G, H) and a character σ of H we consider a generalised Hecke algebra Hσ(G, H), which we study by embedding the given Hecke pair in a Schlichting completion (Gσ, Hσ) that comes equipped with a continuous extension σ on Hσ. The image of σ in Cc(Gσ) is a non-full projection pσ, and Hσ(G, H) is isomorphic to pσCc(Gσ)pσ. We study the structure and properties of C *-completions of a...

C*-Algebra numerical range of quadratic elements

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.