Classifying Polygonal Algebras by their K0-Group

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...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2015-06, Vol.58 (2), p.485-497
Main Authors: Konter, Johan, Vdovina, Alina
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091514000194