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

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 $k$-rank graph C*-algebras, and give explicit examples of $k$-cube groups and their K-theory. We give explicit computations of K-theory for an infinite family of $k$-rank graphs for $k\ge 3$, which is not a direct consequence of the Künneth Theorem for tensor products.

Published version

References in corpus (4)

• Higher rank graph C*-algebras
• Simplicity of C*-algebras associated to higher-rank graphs
• On the K-theory of higher rank graph C*-algebras
• Groups acting on products of trees, tiling systems and analytic K-theory

Cited by in corpus (1)

• Real and complex K-theory for higher rank graph algebras arising from cube complexes