Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid
View through CrossRef
<p>We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we characterise when the C*-algebras of these groupoids are AF embeddable. Our main result generalises theorems in the literature for graphs and for crossed products of commutative C*-algebras by the integers. We give a condition on the surjective local homeomorphism that characterises the AF embeddability of the C*-algebra of the associated Deaconu-Renault groupoid. In order to prove our main result, we analyse homology groups for AF groupoids, and we prove a theorem that gives an explicit formula for the isomorphism of these groups and the corresponding K-theory. This isomorphism generalises FKPS, Matui, since we give an explicit formula for the isomorphism and we show that it preserves positive elements.</p>
Title: AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid
Description:
<p>We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we characterise when the C*-algebras of these groupoids are AF embeddable.
Our main result generalises theorems in the literature for graphs and for crossed products of commutative C*-algebras by the integers.
We give a condition on the surjective local homeomorphism that characterises the AF embeddability of the C*-algebra of the associated Deaconu-Renault groupoid.
In order to prove our main result, we analyse homology groups for AF groupoids, and we prove a theorem that gives an explicit formula for the isomorphism of these groups and the corresponding K-theory.
This isomorphism generalises FKPS, Matui, since we give an explicit formula for the isomorphism and we show that it preserves positive elements.
</p>.
Related Results
The Weil Algebra and the Weil Model
The Weil Algebra and the Weil Model
This chapter evaluates the Weil algebra and the Weil model. The Weil algebra of a Lie algebra g is a g-differential graded algebra that in a definite sense models the total space E...
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Lukasiewicz Fuzzy BM-Algebra and BM-Ideal
Lukasiewicz Fuzzy BM-Algebra and BM-Ideal
Introduction: ℱ???????????????? Sets is a mathematical framework that expands the traditional concept of sets by enabling elements to have degrees of membership. This enables parti...
Irish 14-year-old students’ knowledge of initial algebra
Irish 14-year-old students’ knowledge of initial algebra
Initial algebra is a critical stage in the teaching of algebra and occurs when students are transitioning from arithmetic to algebra. Irish mathematics education at post-primary le...
Minimal Inclusions of C*-algebras of Groupoids
Minimal Inclusions of C*-algebras of Groupoids
<p><strong>A non-degenerate inclusion of C*-algebras B ⊂ A is considered minimal if the only fully normalised ideals are trivial. An ideal is fully normalised if the se...
Finitely Presented Heyting Algebras
Finitely Presented Heyting Algebras
In this paper we study the structure of finitely presented Heyting<br />algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every s...
The Roger–Yang skein algebra and the decorated Teichmüller space
The Roger–Yang skein algebra and the decorated Teichmüller space
Based on hyperbolic geometric considerations, Roger and Yang introduced an extension of the Kauffman bracket skein algebra that includes arcs. In particular, their skein algebra is...
Power Matrices and Dunn-Belnap Semantics: Reflections on a Remark of Graham Priest
Power Matrices and Dunn-Belnap Semantics: Reflections on a Remark of Graham Priest
The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the 'logical matrix' sense) whose underlying a...