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kuntz–krieger algebras

Proceedings of the Edinburgh Mathematical Society (1)

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Classifying Polygonal Algebras by their K0-Group
Part of
- Selfadjoint operator algebras
- $K$-theory and operator algebras
Johan Konter, Alina Vdovina
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 2 / June 2015

Published online by Cambridge University Press:

13 February 2015, pp. 485-497
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We prove that every incidence graph of a finite projective plane allows a partitioning into incident point-line pairs. This is used to determine the order of the identity in the K0-group of so-called polygonal algebras associated with cocompact group actions on Ã2-buildings with three orbits. These C*-algebras are classified by the K0-group and the class of the identity in K0. To be more precise, we show that 2(q − 1) = 0, where q is the order of the links of the building. Furthermore, if q = 22l−1 with l ∈ ℤ, then the order of is q − 1.