Related papers: C*-algebras associated to shift spaces

We characterize the pairs of operator spaces which occur as pairs of Morita equivalence bimodules between non-selfadjoint operator algebras in terms of the mutual relation between the spaces. We obtain a characterization of the operator…

We initiate the program of extending to higher-rank graphs ($k$-graphs) the geometric classification of directed graph $C^*$-algebras, as completed in the 2016 paper of Eilers, Restorff, Ruiz, and Sorensen [ERRS16]. To be precise, we…

The usual crossed product construction which associates to the homeomorphism $T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended to the case of a partial local homeomorphism $T$. For example, the Cuntz-Krieger…

We introduce a class of subshifts under the name of "standard one-counter shifts". The standard one-counter shifts are the Markov coded systems of certain Markov codes that belong to the family of one-counter languages. We study topological…

In this paper we consider algebras with involution over a ring C which is given by the quadratic extension by i of an ordered ring R. We discuss the *-representation theory of such *-algebras on pre-Hilbert spaces over C and develop the…

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show…

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime…

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. Applications include a generalization of the well-known result of Muhly and Solel: Morita equivalent $C^*$-correspondences have Morita equivalent…

We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz-Pimsner…

These lecture notes on $C^{*}$-algebras were prepared for a couple of courses given by the author at IMSc and also at IIT Gandhinagar. The topics covered are: Gelfand-Naimark theorems, universal C*-algebras, Hilbert C*-modules, crossed…

We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two…

We generalize the classification result of Restorff on Cuntz-Krieger algebras to cover all unital graph C*-algebras with real rank zero, showing that Morita equivalence in this case is determined by ordered, filtered K-theory as conjectured…

A certain synchronizing property for subshifts called $\lambda$-synchronization yields $\lambda$-graph systems called the $\lambda$-synchronizing $\lambda$-graph systems for the subshifts. The $\lambda$-synchronizing $\lambda$-graph system…

This note extends and strengthens a theorem of Bates that says that row-finite graphs that are strong shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our stronger notion of Morita equivalence does in…

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…

It is well known that "bad" quotient spaces (typically: non-Hausdorff) can be studied by associating to them the groupoid C*-algebra of an equivalence relation, that in the "nice" cases is Morita equivalent to the C*-algebra of continuous…

We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C*-correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of C*-correspondences.…

In this paper, we will introduce notions of relative version of imprimitivity bimodules and relative version of strong Morita equivalence for pairs of $C^*$-algebras $(\mathcal{A}, \mathcal{D})$ such that $\mathcal{D}$ is a $C^*$-subalgebra…