Uniqueness Theorems for Steinberg Algebras

TL;DR

This paper establishes key uniqueness theorems for Steinberg algebras, characterizes their simplicity via groupoid properties, and describes their centers, advancing the algebraic understanding of groupoid-based structures.

Contribution

It proves Cuntz-Krieger and graded uniqueness theorems, and characterizes the simplicity and centers of Steinberg algebras using groupoid properties.

Findings

Steinberg algebras are basically simple iff their groupoids are effective and minimal.

The paper proves Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras.

It characterizes the center of Steinberg algebras associated to minimal groupoids.

Abstract

We prove Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras. We also show that a Steinberg algebra is basically simple if and only if its associated groupoid is both effective and minimal. Finally we use results of Steinberg to characterise the center of Steinberg algebras associated to minimal groupoids