Classifying Polygonal Algebras by their K0-Group. Issue 2 (13th February 2015)

• Record Type: Journal Article
• Authors: Konter, Johan; Vdovina, Alina
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 58:Issue 2(2015)
• Page Start: 485
• Page End: 497
• Publication Date: 2015-02-13
• Subjects: Euclidean buildings, -- Kuntz–Krieger algebras, -- incidence graphs, -- finite projective planes; Primary 46L80, -- Secondary 19K99; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091514000194
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: 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 K 0 -group of so-called polygonal algebras associated with cocompact group actions on à 2 -buildings with three orbits. These C *-algebras are classified by the K 0 -group and the class of the identity in K 0 . 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 = 2 2 l −1 with l ∈ ℤ, then the order of is q − 1.