arXiv subjects

Bernhard Burgstaller

Publications and source records attributed to Bernhard Burgstaller.

21 records · Page 2Linked to original sources

arXiv2011

On certain properties of Cuntz--Krieger type algebras

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, the ideal structure is studied, % and applied to semigraph algebras, and nuclearity is proved by presenting the algebra as a crossed product of an AF-algebra by an abelian group. The results are applied to examples of Cuntz--Krieger type algebras, such as higher rank semigraph $C^*$-algebras and higher rank Exel-Laca algebras.

math.OA↗

arXiv2011

A descent homomorphism for semimultiplicative sets

We define and provide some basic analysis of various types of crossed products by semimultiplicative sets, and then prove a $KK$-theoretical descent homomorphisms for semimultiplicative sets in accord with the descent homomorphism for discrete groups.

math.OA↗

arXiv2011

A Cuntz--Krieger uniqueness theorem for semigraph $C^*$-algebras

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 ultragraph algebras. We prove Cuntz--Krieger uniqueness theorems for cancelling semigraph algebras and aperiodic full semigraph algebras.

math.OA↗