C ⋆ -algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory

• Autores: Sam A. Mutter, Aura-Cristiana Radu, Alina Vdovina
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 1, 2024, págs. 187-217
• Idioma: inglés
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• Resumen

  • We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called k-cube groups, which act freely and transitively on the product of k trees, for arbitrary k. The quotient of this action on the product of trees defines a k-dimensional cube complex,which induces a higher-rank graph. We make deductions about the K-theory of the corresponding rank-k graph C?-algebras, and give examples of k-cube groups and their K-theory. These are among the first explicit computations of K-theory for an infinite family of rank-k graphs for k ≥ 3, which isnot a direct consequence of the K¨unneth theorem for tensor products.