arXiv subjects
Publications and source records attributed to Klaus Thomsen.
It shown that an a locally injective surjection on a compact metric space admits a canonical locally homeomorphic extension such that the associated C*-algebras are isomorphic. This is then used in a study of the possible inverse temperatures of KMS states for a generalized gauge action.
We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan subalgebras, we obtain results which both generalize and improve on the corresponding results from the 'etale case. In the second part we apply the results to dynamical systems and subshifts.
We prove that the unitary equivalence classes of extensions of C*_r(G) by any sigma-unital stable C"-algebra, taken modulo extensions which split via an asymptotic homomorphism, form a group which can be calculated from the universal coefficient theorem of KK-theory when G is a free product of a countable collection of amenable groups.
It is shown that the heteroclinic and homoclinic algebras of a generalized one-dimensional solenoid are simple AH-algebras of real rank zero with no dimension growth and a unique trace. In the orientable case they are AT-algebras, and in the non-orientable case they have two-torsion both in K_1 and K_0.
Let $A$ and $B$ be separable $C^*$-algebras, $A$ unital and $B$ stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of $A$ by $B$ to the group which arises by restricting the attention to \emph{unital} semi-split extensions of $A$ by $B$. The six-terms exact sequence is an unpublished result of G. Skandalis.
Let A and B be $C^*$-algebras, A separable, and B $σ$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot,\cdot]$ denotes the set of homotopy classes of *-homomorphisms, $Q(B) = M(B)/B$ is the generalized Calkin algebra and K denotes the $C^*$-algebra of compact operators.