Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Exel's Crossed Product For Non-Unital C*-Algebras, Nathan D. Brownlowe, Iain F. Raeburn, Sean T. Vittadello
Exel's Crossed Product For Non-Unital C*-Algebras, Nathan D. Brownlowe, Iain F. Raeburn, Sean T. Vittadello
Faculty of Informatics - Papers (Archive)
We consider a family of dynamical systems (A, alpha, L) in which a is an endomorphism of a C*-algebra A and L is a transfer operator for a. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show that the C*-algebra of a locally finite graph can be realised as one of these crossed products. When A is commutative, we find criteria for the simplicity of the crossed product, and analyse the ideal structure of the crossed product.
C*-Algebras Of Tilings With Infinite Rotational Symmetry, Michael F. Whittaker
C*-Algebras Of Tilings With Infinite Rotational Symmetry, Michael F. Whittaker
Faculty of Informatics - Papers (Archive)
A tiling with infinite rotational symmetry, such as the Conway– Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an etale equivalence relation is associated. A groupoid C¤-algebra for a tiling is produced and a separating dense set is exhibited in the C*-algebra which encodes the structure of the topological dynamical system. In the case of a substitution tiling, natural subsets of this separating dense set are used to define an AT-subalgebra of the C*-algebra. Finally our results are applied to the Pinwheel Tiling.
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.