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Full-Text Articles in Physical Sciences and Mathematics
The Co-Universal C*-Algebra Of A Row-Finite Graph, Aidan Sims
The Co-Universal C*-Algebra Of A Row-Finite Graph, Aidan Sims
Faculty of Informatics - Papers (Archive)
Let $E$ be a row-finite directed graph. We prove that there exists a $C^*$-algebra $\Cr{E}$ with the following co-universal property: given any $C^*$-algebra $B$ generated by a Toeplitz-Cuntz-Krieger $E$-family in which all the vertex projections are nonzero, there is a canonical homomorphism from $B$ onto $\Cr{E}$. We also identify when a homomorphism from $B$ to $\Cr{E}$ obtained from the co-universal property is injective. When every loop in $E$ has an entrance, $\Cr{E}$ coincides with the graph $C^*$-algebra $C^*(E)$, but in general, $\Cr{E}$ is a quotient of $C^*(E)$. We investigate the properties of $\Cr{E}$ with emphasis on the utility of co-universality …
Phase Transition On The Toeplitz Algebra Of The Affine Semigroup Over The Natural Numbers, Marcelo Laca, Iain F. Raeburn
Phase Transition On The Toeplitz Algebra Of The Affine Semigroup Over The Natural Numbers, Marcelo Laca, Iain F. Raeburn
Faculty of Informatics - Papers (Archive)
We show that the group of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup N⋊N×. The associated Toeplitz C∗-algebra T(N⋊N×) is universal for isometric representations which are covariant in the sense of Nica. We give a presentation of T(N⋊N×) in terms of generators and relations, and use this to show that the C∗-algebra QN recently introduced by Cuntz is the boundary quotient of in the sense of Crisp and Laca. The Toeplitz algebra T …