Crossed products of k-graph C*-algebras by Z^l

TL;DR

This paper constructs higher-rank graph C*-algebras from actions of Z^l on k-graph C*-algebras and analyzes their structure, expanding understanding of crossed product constructions in operator algebras.

Contribution

It introduces a method to build (k+l)-graph C*-algebras from Z^l actions on k-graph C*-algebras, providing a new framework for studying crossed products.

Findings

Construction of (k+l)-graph from Z^l action

Identification of the crossed product with a higher-rank graph C*-algebra

Structural analysis of the resulting crossed product C*-algebra

Abstract

An action of Z^l by automorphisms of a k-graph induces an action of Z^l by automorphisms of the corresponding k-graph C*-algebra. We show how to construct a (k+l)-graph whose C*-algebra coincides with the crossed product of the original k-graph algebra by Z^l. We then investigate the structure of the crossed-product C*-algebra.