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Full-Text Articles in Science and Technology Studies
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Associate Professor Adam Rennie
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Associate Professor Adam Rennie
We construct a family of purely infinite C¤-algebras, Q¸ for ¸ 2 (0, 1) that are classified by their K-groups. There is an action of the circle T with a unique KMS state à on each Q¸. For ¸ = 1/n, Q1/n »= On, with its usual T action and KMS state. For ¸ = p/q, rational in lowest terms, Q¸ »= On (n = q − p + 1) with UHF fixed point algebra of type (pq)1. For any n > 1, Q¸ »= On for infinitely many ¸ with distinct KMS states and UHF fixed-point algebras. For any ¸ …
Catalytic Role Of Ge In Highly Reversible Geo2/Ge/C Nanocomposite Anode Material For Lithium Batteries, Kuok Hau Seng, Mi-Hee Park, Zai Ping Guo, Hua-Kun Liu, Jaephil Cho
Catalytic Role Of Ge In Highly Reversible Geo2/Ge/C Nanocomposite Anode Material For Lithium Batteries, Kuok Hau Seng, Mi-Hee Park, Zai Ping Guo, Hua-Kun Liu, Jaephil Cho
Faculty of Engineering and Information Sciences - Papers: Part A
GeO2/Ge/C anode material synthesized using a simple method involving simultaneous carbon coating and reduction by acetylene gas is composed of nanosized GeO2/Ge particles coated by a thin layer of carbon, which is also interconnected between neighboring particles to form clusters of up to 30 μm. The GeO2/Ge/C composite shows a high capacity of up to 1860 mAh/g and 1680 mAh/g at 1 C (2.1 A/g) and 10 C rates, respectively. This good electrochemical performance is related to the fact that the elemental germanium nanoparticles present in the composite increases the reversibility of the conversion reaction of GeO2. These factors have …
A Unique Sandwich-Structured C/Ge/Graphene Nanocomposite As An Anode Material For High Power Lithium Ion Batteries, Dan Li, Kuok H. Seng, Dongqi Shi, Zhixin Chen, Hua-Kun Liu, Zaiping Guo
A Unique Sandwich-Structured C/Ge/Graphene Nanocomposite As An Anode Material For High Power Lithium Ion Batteries, Dan Li, Kuok H. Seng, Dongqi Shi, Zhixin Chen, Hua-Kun Liu, Zaiping Guo
Faculty of Engineering and Information Sciences - Papers: Part A
A unique sandwich-structured C/Ge/graphene composite with germanium nanoparticles trapped between graphene sheets is prepared by a microwave-assisted solvothermal reaction followed by carbon coating and thermal reduction. The graphene sheets are found to be effective in hindering the growth and aggregation of GeO2 nanoparticles. More importantly, the graphene sheets, coupled with the carbon coating, can buffer the volume changes of germanium in electrochemical lithium reactions. The unique sandwich structure features a highly conductive network of carbon, which can improve both the conductivity and the structural stability of the electrode material, and exemplifies a promising strategy for the development of new high …
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Faculty of Engineering and Information Sciences - Papers: Part A
Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated with a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph. is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of …
On The K-Theory Of Twisted Higher-Rank-Graph C*-Algebras, Alex Kumjian, David Pask, Aidan Sims
On The K-Theory Of Twisted Higher-Rank-Graph C*-Algebras, Alex Kumjian, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the K-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value βc, we give an explicit construction of all the KMSβ states. If the graph is strongly connected, then there is a unique KMSβc state, and this state factors through the quotient map onto C*(E). Our approach is direct and relatively elementary.