Open Access. Powered by Scholars. Published by Universities.^{®}

#
Social and Behavioral Sciences *Commons*^{™}

Open Access. Powered by Scholars. Published by Universities.^{®}

Articles **1** - **9** of ** 9**

## Full-Text Articles in Social and Behavioral Sciences

Nonlocal Transistor Based On Pure Crossed Andreev Reflection In A Euo-Graphene/Superconductor Hybrid Structure, Yee Sin Ang, Lawrence Ang, C Zhang, Zhongshui Ma

#### Nonlocal Transistor Based On Pure Crossed Andreev Reflection In A Euo-Graphene/Superconductor Hybrid Structure, Yee Sin Ang, Lawrence Ang, C Zhang, Zhongshui Ma

*Faculty of Engineering and Information Sciences - Papers: Part A*

We study the interband transport in a superconducting device composed of graphene with EuO-induced exchange interaction. We show that pure crossed Andreev reflection can be generated exclusively without the parasitic local Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi levels in an EuO-graphene/superconductor/EuO-graphene device. The pure nonlocal conductance exhibits rapid on-off switching and oscillatory behavior when the Fermi levels in the normal and the superconducting leads are varied. The oscillation reflects the quasiparticle propagation in the superconducting lead and can be used as a tool to probe the subgap quasiparticle mode in superconducting graphene, which …

Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn

#### Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn

*Faculty of Engineering and Information Sciences - Papers: Part A*

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.

Purely Infinite Partial Crossed Products, Thierry Giordano, Adam Sierakowski

#### Purely Infinite Partial Crossed Products, Thierry Giordano, Adam Sierakowski

*Faculty of Engineering and Information Sciences - Papers: Part A*

Let (A, G, alpha) be a partial dynamical system. We show that there is a bijective corespondence between G-invariant ideals of A and ideals in the partial crossed prroduct A xalpha, r G provided the action is exact and residually topologically free.

Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe

#### Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe

*Faculty of Engineering and Information Sciences - Papers: Part A*

We use the boundary-path space of a finitely-aligned k-graph Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C*(Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it to be NO(X). We then compare this crossed product with other definitions in the literature.

Purely Infinite C-Algebras Arising From Crossed Products, Mikael Rordam, Adam Sierakowski

#### Purely Infinite C-Algebras Arising From Crossed Products, Mikael Rordam, Adam Sierakowski

*Faculty of Engineering and Information Sciences - Papers: Part A*

We study conditions that will ensure that a crossed product of a C-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C-algebra is a Kirchberg algebra in the …

The Ideal Structure Of Reduced Crossed Products, Adam Sierakowski

#### The Ideal Structure Of Reduced Crossed Products, Adam Sierakowski

*Faculty of Engineering and Information Sciences - Papers: Part A*

Let (A, G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine suﬃcient—and in some cases also necessary—conditions for A to separate the ideals in A ⋊r G. When A separates the ideals in A ⋊r G, then there is a one-to-one correspondence between the ideals in A ⋊r G and the invariant ideals in A. We extend the concept of topological freeness and present a generalization of the Rokhlin property. Exactness properties of (A, G) turns out to be crucial in these …

Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn

#### Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn

*Faculty of Engineering and Information Sciences - Papers: Part A*

We consider Exel's new construction of a crossed product of a $C^*$-algebra $A$ by an endomorphism $\alpha$. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be realised as a relative Cuntz-Pimsner algbera. We describe a necessary and sufficient condition for the canonical map from $A$ into the crossed product to be injective, and present several examples to demonstrate the scope of this result. We also prove a gauge-invariant uniqueness theorem for the crossed product.

Crossed Products By Semigroups Of Endomorphisms And The Toeplitz Algebras Of Ordered Groups, Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn

#### Crossed Products By Semigroups Of Endomorphisms And The Toeplitz Algebras Of Ordered Groups, Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn

*Faculty of Engineering and Information Sciences - Papers: Part A*

No abstract provided.

Representations Of Crossed Products By Coactions And Principal Bundles, M B. Landstad, J Phillips, Iain Raeburn, C E. Sutherland

#### Representations Of Crossed Products By Coactions And Principal Bundles, M B. Landstad, J Phillips, Iain Raeburn, C E. Sutherland

*Faculty of Engineering and Information Sciences - Papers: Part A*

The main purpose of this paper is to establish a covariant representation theory for coactions of locally compact groups on C^{*}-algebras (including a notion of exterior equivalence), to show how these results extend the usual notions for actions of groups on C^{*}-algebras, and to apply these ideas to classes of coactions termed pointwise unitary and locally unitary to obtain a complete realization of the isomorphism theory of locally trivial principal G-bundles in this context. We are also able to obtain all (Cartan) principal G-bundles in this context, but their isomorphism theory remains elusive.