Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras

By Ben Steinberg. 2014

59 citations recorded by the source corpus.

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and can be used to recover the known primitivity criterion for Leavitt path algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/abc976a52fce1ac131a864ec678e9071dba38338

Citations in the corpus

• Simplicity of algebras associated to non-Hausdorff groupoids (2018, unknown): “ be non-Hausdorff, as we will see in examples of subsections 5.5 and 5.6. In [12, Theorem 3.15] are given criteria on α which are equivalent to G(α) being Hausdorff. This problem was also considered in [28]. An inverse semigroup acts on its tight spectrum. Let Dθ e = {ξ ∈ Eb tight(S) : e ∈ ξ} = U({e},”