C ⋆ -algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory
Mutter, Sam A. (Newcastle University. School of Mathematics, Statistics and Physics)
Radu, Aura-Cristiana (Newcastle University. School of Mathematics, Statistics and Physics)
Vdovina, Alina (Newcastle University. School of Mathematics, Statistics and Physics)

Date:	2024
Abstract:	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 is not a direct consequence of the K¨unneth theorem for tensor products.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Higher-rank graphs ; Graph algebras ; K-theory ; Buildings
Published in:	Publicacions matemàtiques, Vol. 68 Núm. 1 (2024) , p. 187-217 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/422939
DOI: 10.5565/PUBLMAT6812408

31 p, 699.1 KB

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