639 research outputs found
Simplicity of algebras associated to \'etale groupoids
We prove that the C*-algebra of a second-countable, \'etale, amenable
groupoid is simple if and only if the groupoid is topologically principal and
minimal. We also show that if G has totally disconnected unit space, then the
associated complex *-algebra introduced by Steinberg is simple if and only if
the interior of the isotropy subgroupoid of G is equal to the unit space and G
is minimal.Comment: The introduction has been updated and minor changes have been made
throughout. To appear in Semigroup Foru
Smarandache fantastic ideals of Smarandache BCI-algebras
The notion of Smarandache fantastic ideals is introduced, examples are given,
and related properties are investigated. Relations among Q-Smarandache fresh ideals, Q-Smarandache clean ideals and Q-Smarandache fantastic ideals are given. A characterization of a Q-Smarandache fantastic ideal is provided. The extension property for Q-Smarandache fantastic ideals is established
The primitive ideals of some \'etale groupoid C*-algebras
Consider the Deaconu-Renault groupoid of an action of a finitely generated
free abelian monoid by local homeomorphisms of a locally compact Hausdorff
space. We catalogue the primitive ideals of the associated groupoid C*-algebra.
For a special class of actions we describe the Jacobson topology.Comment: 22 page
Invertibility in groupoid C*-algebras
Given a second-countable, Hausdorff, \'etale, amenable groupoid G with
compact unit space, we show that an element a in C*(G) is invertible if and
only if \lambda_x(a) is invertible for every x in the unit space of G, where
\lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also
prove that, for every a in C*(G), there exists some x in G^{(0)} such that
||a|| = ||\lambda_x(a)||.Comment: 8 page
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