Cycline subalgebras of $k$-graph C*-algebras

TL;DR

This paper proves that cycline subalgebras in $k$-graph C*-algebras are maximal abelian and characterizes when they are Cartan subalgebras, enhancing understanding of their structure.

Contribution

It establishes maximal abelianness of cycline subalgebras and provides criteria for when they are Cartan subalgebras in $k$-graph C*-algebras.

Findings

Cycline subalgebras are maximal abelian.

Conditions for cycline subalgebras to be Cartan.

Improved structural understanding of $k$-graph C*-algebras.

Abstract

In this paper, we prove that the cycline subalgbra of a $k$-graph C*-algebra is maximal abelian, and show when it is a Cartan subalgebra (in the sense of Renault).