Uniqueness Theorems for Steinberg Algebras

By L. O. Clark, Cain Edie-Michell. 2014

54 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78ce41a744df2f378b8a8512a51eba59a34190f1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Roozbeh Hazrat
2. Ben Steinberg
3. Huanhuan Li
4. P. Ara
5. Aidan Sims
6. G. Abrams
7. Alexei Stepanov
8. R. Exel

In Mathematical Physics

1. Roozbeh Hazrat
2. Aidan Sims
3. Huanhuan Li
4. P. Ara
5. Ben Steinberg
6. R. Exel
7. L. O. Clark
8. G. Abrams

Citations in the corpus

• Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras (2014, background): “ χV ∗Ψ∗χV = 0 because VKV = ∅. Thus χV ∗ψ∗χV = χV ∗ψ|G(0) ∗χV = k1 ·χV is in I, as required. Our next result removes the Hausdorff condition from a result of [4] and works over any base ring. See also [5] where more or less the same result is obtained in a slightly different way. ETALE GROUPOID ALGEBR”
• Graded Steinberg algebras and their representations (2017, background): “By [Clark and Edie-Michell 2015, Lemma 2.2; Clark et al. 2014, Lemma 3.5], every element f ∈ A R ( G ) can be expressed as where F is a finite subset of mutually disjoint elements of”