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Full-Text Articles in Science and Technology Studies
Representations Of Cuntz-Pimsner Algebras, Neal J. Fowler, Paul S. Muhly, Iain Raeburn
Representations Of Cuntz-Pimsner Algebras, Neal J. Fowler, Paul S. Muhly, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Let X be a Hilbert bimodule over a C * -algebra A. We analyse the structure of the associated Cuntz-Pimsner algebra X and related algebras using representation-theoretic methods. In particular, we study the ideals (I) in X induced by appropriately invariant ideals I in A, and identify the quotients X/(I) as relative Cuntz-Pimsner algebras of Muhly and Solel. We also prove a gauge-invariant uniqueness theorem for X, and investigate the relationship between X and an alternative model proposed by Doplicher, Pinzari and Zuccante.
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterises the higher-rank graphs that admit a nontrivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.