arXiv subjects
Publications and source records attributed to Enrique Pardo.
In this note we show that a combinatorial model of Kirchberg algebras in the UCT, namely the Katsura algebras O_{AB}, can be expressed both as groupoid C*-algebras and as inverse semigroup crossed products. We use this picture to obtain results about simplicity, pure infiniteness and nuclearity of O_{AB} using different methods than those used by Katsura.
In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid $S$ acting on a unital ring $A$ by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup $C^*$-crossed products.
Necessary and sufficient conditions for when every non-zero ideal in a relative Cuntz-Pimsner ring contains a non-zero graded ideal, when a relative Cuntz-Pimsner ring is simple, and when every ideal in a relative Cuntz-Pimsner ring is graded, are given. A "Cuntz-Krieger uniqueness theorem" for relative Cuntz-Pimsner rings is also given and condition (L) and condition (K) for relative Cuntz-Pimsner rings are introduced.
We describe simplicity of the Stacey crossed product A\times_β\N in terms of conditions of the endomorphism β. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^γ\times_{β_E}\N to study its ideal properties, in terms of the (non-classical) C*-dynamical system (C*(E)^γ, β_E). Finally, we give sufficient conditions for the Stacey crossed product A\times_β\N being a purely infinite simple C*-algebra.
We prove that the Higman-Thompson groups $G_{n,r}^+$ and $G_{m,s}^+$ are isomorphic if and only if $m=n$ and $\mbox{gcd}(n-1,r)=\mbox{gcd}(n-1,s)$.
We give an elementary characterization of those (abelian) semigroups $M$ that are direct limits of countable sequences of finite direct products of monoids of the form $C\cup\{0\}$ for monogenic groups $C$. This characterization involves the Riesz refinement property together with lattice-theoretical properties of the collection of subgroups of $M$, and it makes it possible to express $M$ as a certain submonoid of a direct product $S\times G$, where $S$ is a distributive semilattice with zero and $G$ is an abelian group. When applied to the monoids $V(A)$ appearing in the nonstable K-theory of C*-algebras, our results yield a full description of $V(A)$ for C*-inductive limits $A$ of finite products of full matrix algebras over either Cuntz algebras $O\_n$, where $2\leq n<\infty$, or corners of $O\_{\infty}$ by projections, thus extending to the case including $O\_{\infty}$ earlier work by the authors together with K.R. Goodearl.