5 citations · 16 across the 16 of their papers we have counts for
21 papers
The universal property of graded -theory
Bernhard Burgstaller
To each Kasparov cycle we attach inclusions satisfying . A lift of a second factor along therefore re…
Computing the -homology -theory product in splitexact algebraic -theory
Bernhard Burgstaller
Explicit formulas are indicated that compute the product of a level-one element and any element in splitexact algebraic…
Corner embeddings into algebras of compact operators in -theory
Bernhard Burgstaller
We show that in -theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK…
On the -theory in splitexact algebraic -theory
Bernhard Burgstaller
It is proven that in the universal splitexact equivariant algebraic -theory for algebras, the -theory groups coincide with classical -theory in the sense of Phillips. Thi…
Information content in formal languages
Bernhard Burgstaller
Motivated by creating physical theories, formal languages with variables are considered and a kind of distance between elements of the languages is defined by the formula $d(x,…
A kind of -theory for rings
Bernhard Burgstaller
A group equivariant -theory for rings will be defined and studied in analogy to Kasparov's -theory for -algebras. It is a kind of linearization of the category of ring…
Aspects of equivariant -theory in its generators and relations picture
Bernhard Burgstaller
We give a new proof of the universal property of -theory with respect to stability, homotopy invariance and split-exactness for a locally compact group, or a locally comp…
Some remarks in - and -theory
Bernhard Burgstaller
This note consists of three unrelated remarks. First, we demonstrate how roughly speaking -homomorphisms between matrix stable -algebras are exactly the uniformly continuou…
Semigroup homomorphisms on matrix algebras
Bernhard Burgstaller
We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or -algebras.
A note on a certain Baum--Connes map for inverse semigroups
Bernhard Burgstaller
Let denote a countable inverse semigroup. We construct a kind of a Baum--Connes map by a categorial approach via localization…
The generators and relations picture of -theory
Bernhard Burgstaller
This is half an overview article since what we describe here is essentially known. We describe -theory by generators and relations in a formal sum of formal products of -hom…
Inverse semigroup equivariant -theory and -extensions
Bernhard Burgstaller
In this note we extend the classical result by G. G. Kasparov that the Kasparov groups can be identified with the extension groups $\mbox{Ext}(A,B)$ to the inverse semi…
Attempts to define a Baum--Connes map via localization of categories for inverse semigroups
Bernhard Burgstaller
Meyer and Nest showed that the Baum--Connes map is equivalent to a map on -theory of two different crossed products. This approach is strongly categorial in method since its bas…
A Green--Julg isomorphism for inverse semigroups
Bernhard Burgstaller
For every finite unital inverse semigroup and --algebra we establish an isomorphism between and . This extends the classical Gr…
An elementary Green imprimitivity theorem for inverse semigroups
Bernhard Burgstaller
A Morita equivalence similar to that found by Green for crossed products by groups will be established for crossed products by inverse semigroups. More precisely, let be an inv…
The universal property of inverse semigroup equivariant -theory
Bernhard Burgstaller
Higson proved that every homotopy invariant, stable and split exact functor from the category of -algebras to an additive category factors through Kasparov's -theory. By a…
Equivariant -theory of -discrete groupoids and inverse semigroups
Bernhard Burgstaller
For an -discrete Hausdorff groupoid and an inverse semigroup of slices of there is an isomorphism between -equivariant -theory and compat…
On certain properties of Cuntz--Krieger type algebras
Bernhard Burgstaller
The note presents a further study of the class of Cuntz--Krieger type algebras. A necessary and sufficient condition is identified that ensures that the algebra is purely infinite,…
A Cuntz--Krieger uniqueness theorem for semigraph -algebras
Bernhard Burgstaller
Higher rank semigraph algebras are introduced by mixing concepts of ultragraph algebras and higher rank graph algebras. This yields a kind of higher rank generalisation of ultragra…
A descent homomorphism for semimultiplicative sets
Bernhard Burgstaller
We define and provide some basic analysis of various types of crossed products by semimultiplicative sets, and then prove a -theoretical descent homomorphisms for semimultiplic…
On freely generated semigraph -algebras
Bernhard Burgstaller
For special universal -algebras associated to -semigraphs we present the universal representations of these algebras, prove a Cuntz--Krieger uniqueness theorem, and compute…