Regular Ideals of Locally-Convex Higher-Rank Graph Algebras

TL;DR

This paper characterizes regular ideals in locally-convex higher-rank graph algebras, showing their properties and how they relate to conditions like (B), with implications for both algebraic and C*-algebraic structures.

Contribution

It provides a vertex set description for regular ideals and demonstrates the preservation of Condition (B) under quotients, extending results to C*-algebras.

Findings

Vertex set description for regular ideals

Condition (B) preserved under quotients

All regular ideals are graded under certain conditions

Abstract

We give a vertex set description for basic, graded, regular ideals of locally-convex Kumjian-Pask Algebras. We also show that Condition (B) is preserved when taking the quotient by a basic, graded, regular ideal. We further show that when a locally-convex, row-finite k-graph satisfies Condition (B), all regular ideals are graded. We then show the same things hold for gauge-invariant, regular ideals in locally-convex k-graph C*-algebras.