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Classifying Polygonal Algebras by their K0-Group
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- 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.
of the identity in SEMIFIELDS ARISING FROM IRREDUCIBLE SEMILINEAR TRANSFORMATIONS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 85 / Issue 3 / December 2008
- Published online by Cambridge University Press:
- 01 December 2008, pp. 333-339
- Print publication:
- December 2008
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A construction of finite semifield planes of order n using irreducible semilinear transformations on a finite vector space of size n is shown to produce fewer than
different nondesarguesian planes.
different nondesarguesian planes.