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Joachim Cuntz

Publications and source records attributed to Joachim Cuntz.

23 records · Page 2Linked to original sources
arXiv2006

$C^*$-algebras associated with the $ax+b$-semigroup over $\mathbb N$

We present a $C^*$-algebra which is naturally associated to the $ax+b$-semigroup over $\mathbb N$. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which corresponds to addition. Its stabilization can be described as a crossed product of the algebra of continuous functions, vanishing at infinity, on the space of finite adeles for $\mathbb Q$ by the natural action of the $ax+b$-group over $\mathbb Q$.

math.OA↗
arXiv2005

Algebraic K-theory and locally convex algebras

We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative algebraic K-theory. We develop the technology of Kasparov modules in an algebraic setting in order to obtain the results. The article also includes a computation of the first algebraic K-theory of harmonic operator ideals.

math.KT↗
arXiv2004

Bivariant $K$-theory and the Weyl algebra

We introduce a new version $kk^{\rm alg}$ of bivariant $K$-theory that is defined on the category of all locally convex algebras. A motivating example is the Weyl algebra $W$, i.e. the algebra generated by two elements satisfying the Heisenberg commutation relation, with the fine locally convex topology. We determine its $kk^{\rm alg}$-invariants using a natural extension for $W$. Using similar methods the $kk^{\rm alg}$-invariants can be determined for many other algebras of similar type.

math.KT↗
arXiv2001

Cyclic Theory and the Bivariant Chern-Connes Character

We give a survey of cyclic homology/cohomology theory including a detailed discussion of cyclic theories for various classes of topological algebras. We show how to associate cyclic classes with Fredholm modules and $K$-theory classes and how to construct a completely general bivariant Chern-Connes character from bivariant $K$-theory to bivariant cyclic theory.

math.OA↗