Simplicity, primitivity and semiprimitivity of étale groupoid algebras with applications to inverse semigroup algebras. (English) Zbl 1383.20038
Summary: This paper studies simplicity, primitivity and semiprimitivity of algebras associated to étale 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.
MSC:
| 20M18 | Inverse semigroups |
| 20M25 | Semigroup rings, multiplicative semigroups of rings |
| 16S99 | Associative rings and algebras arising under various constructions |
| 16S36 | Ordinary and skew polynomial rings and semigroup rings |
| 22A22 | Topological groupoids (including differentiable and Lie groupoids) |
Keywords:
simplicity; primitivity; semiprimitivity; étale groupoids; inverse semigroup algebras; Leavitt path algebrasReferences:
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