Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras

AbstractFor a 1-cocycle c on a principal r-discrete groupoid G, that vanishes only on the unit space of G, we show that the asymptotic range of c, , is an invariant for the total order c−1([0, ∞]). It follows that is also an invariant (with respect to isometric isomorphisms) of the triangular analytic algebra supported on c−1([0, ∞]). We also prove that if and only if the analytic algebra has a certain maximality property.

Download Full-text

Dense subalgebras of purely infinite simple groupoid C*-algebras

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091520000036 ◽

2020 ◽

Vol 63 (3) ◽

pp. 609-629

Author(s):

Jonathan H. Brown ◽

Lisa Orloff Clark ◽

Astrid an Huef

Keyword(s):

Characteristic Functions ◽

C Algebras ◽

Unit Space ◽

Intermediate Algebra ◽

Higher Rank

AbstractA simple Steinberg algebra associated to an ample Hausdorff groupoid G is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg algebra is algebraically purely infinite, then the reduced groupoid $C^*$-algebra $C^*_r(G)$ is simple and purely infinite. But the Steinberg algebra seems too small for the converse to hold. For this purpose we introduce an intermediate *-algebra B(G) constructed using corners $1_U C^*_r(G) 1_U$ for all compact open subsets U of the unit space of the groupoid. We then show that if G is minimal and effective, then B(G) is algebraically properly infinite if and only if $C^*_r(G)$ is purely infinite simple. We apply our results to the algebras of higher-rank graphs.

Download Full-text

An Introduction to K-Theory for C*-Algebras

10.1017/cbo9780511623806 ◽

2000 ◽

Cited By ~ 41

Author(s):

M. Rørdam ◽

F. Larsen ◽

N. Laustsen

Keyword(s):

C Algebras ◽

K Theory

Download Full-text

Improving Under-Resourced Language ASR Through Latent Subword Unit Space Discovery

10.21437/interspeech.2016-1010 ◽

2016 ◽

Author(s):

Marzieh Razavi ◽

Mathew Magimai-Doss

Keyword(s):

Unit Space

Download Full-text

Synchronicity II

10.1093/oso/9780198828839.003.0005 ◽

2018 ◽

Author(s):

Lexi Eikelboom

Keyword(s):

Continental Philosophy ◽

Total Order ◽

Radical Orthodoxy ◽

Theological Perspective ◽

Musical Ontology

In contrast to the previous two chapters, which theologically engage rhythm in continental philosophy, this chapter examines Augustine’s explicitly theological approach to rhythm and its various receptions. The chapter uses Przywara’s scheme of intra-creaturely and theological analogies to frame Augustine’s treatment of rhythm in chapter six of De Musica. While Agamben represents an intra-creaturely perspective, Augustine represents a theological perspective. The degree to which this synchronic, theological view, which envisions rhythm as that which binds metaphysical layers of reality together allowing for communication between them, is problematic depends on the degree to which it is uncoupled from an intra-creaturely perspective like that of Agamben. Proponents of Radical Orthodoxy who propose an Augustinian musical ontology represent such an uncoupling, leading to a total order that betrays creatureliness. Erich Przywara’s interpretation, in contrast, retains the tension in Augustine between both the theological perspective on reality as harmonious and the intra-creaturely experience of interruption.

Download Full-text