Klaus Thomsen
KMS states and conformal measures.
Tue, 09/13/2011 - 15:01 — SomNambulAuthors: Klaus Thomsen
Subjects: Operator Algebras
AbstractFrom a non-constant holomorphic map on a connected Riemann surface we
construct an 'etale second countable locally compact Hausdorff groupoid whose
associated groupoid C*-algebra admits a one-parameter group of automorphisms
with the property that its KMS states corresponds to conformal measures in the
sense of Sullivan. In this way certain quadratic polynomials give rise to
quantum statistical models with a phase transition arising from spontaneous
symmetry breaking.Shape theory and extensions of C*-algebras.
Tue, 07/13/2010 - 15:01 — SomNambulAuthors: Klaus Thomsen, Vladimir Manuilov
Subjects: Operator Algebras
AbstractLet $A$, $A'$ be separable $C^*$-algebras, $B$ a stable $\sigma$-unital
$C^*$-algebra. Our main result is the construction of the pairing
$[[A',A]]\times\operatorname{Ext}^{-1/2}(A,B)\to\operatorname{Ext}^{-1/2}(A',B)$,
where $[[A',A]]$ denotes the set of homotopy classes of asymptotic
homomorphisms from $A'$ to $A$ and $\operatorname{Ext}^{-1/2}(A,B)$ is the
group of semi-invertible extensions of $A$ by $B$. Assume that all extensions
of $A$ by $B$ are semi-invertible.On the C*-algebra of a locally injective surjection and its KMS states.
Tue, 12/22/2009 - 16:01 — SomNambulAuthors: Klaus Thomsen
Subjects: Operator Algebras
AbstractIt 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.Semi etale groupoids and applications.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Klaus Thomsen
Subjects: Operator Algebras
AbstractWe 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.
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