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Full-Text Articles in Physical Sciences and Mathematics
Periodic 2-Graphs Arising From Subshifts, David Pask, Iain Raeburn, Natasha A. Weaver
Periodic 2-Graphs Arising From Subshifts, David Pask, Iain Raeburn, Natasha A. Weaver
Faculty of Informatics - Papers (Archive)
Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz– Krieger algebras. In a previous paper, we constructed 2 graphs whose path spaces are rank two subshifts of finite type, and showed that this construction yields aperiodic 2 graphs whose C algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2 graphs which we call domino graphs. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the C algebras …
Aperiodicity And Cofinality For Finitely Aligned Higher-Rank Graphs, Peter Lewin, Aidan Sims
Aperiodicity And Cofinality For Finitely Aligned Higher-Rank Graphs, Peter Lewin, Aidan Sims
Faculty of Informatics - Papers (Archive)
We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs $\Lambda$, and prove that $C^*(\Lambda)$ is simple if and only if $\Lambda$ is aperiodic and cofinal. The main advantage of our versions of aperiodicity and cofinality over existing ones is that ours are stated in terms of finite paths. To prove our main result, we first characterise each of aperiodicity and cofinality of $\Lambda$ in terms of the ideal structure of $C^*(\Lambda)$. In an appendix we show how our new cofinality condition simplifies in a number of special cases which have been treated previously in the literature; …
A Direct Approach To Co-Universal Algebras Associated To Directed Graphs, Aidan Sims, S B. Webster
A Direct Approach To Co-Universal Algebras Associated To Directed Graphs, Aidan Sims, S B. Webster
Faculty of Informatics - Papers (Archive)
We prove directly that if $E$ is a directed graph in which every cycle has an entrance, then there exists a $C^*$-algebra which is co-universal for Toeplitz-Cuntz-Krieger $E$-families. In particular, our proof does not invoke ideal-structure theory for graph algebras, nor does it involve use of the gauge action or its fixed point algebra.