Related papers: Quasifolds, Diffeology and Noncommutative Geometry

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are…

We study the groupoid C*-algebras associated to the equivalence relation induced by a quotient map on a locally compact Hausdorff space. This C*-algebra is always a Fell algebra, and if the quotient space is Hausdorff, it is a…

We use the dimension and the Lie algebra structure of the first Hochschild cohomology group to distinguish some algebras of dihedral, semi-dihedral and quaternion type up to stable equivalence of Morita type. In particular, we complete the…

We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…

This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example of description of the structure of C*-algebras of…

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

Let $A \subset C$ and $B \subset D$ be unital inclusions of unital $C^*$-algebras. Let ${}_A \mathbf{B}_A (C, A)$ (resp. ${}_B \mathbf{B}_B (D, B)$) be the space of all bounded $A$-bimodule (resp. $B$-bimodule) linear maps from $C$ (resp.…

To a formally smooth algebra A we associate a quiver setting (Q,a) containing enough information to reconstruct all the local quiver settings determining the etale local structure of finite dimensional representation schemes of A, see…

In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. In particular, give a new proof of Caldararu's conjecture about Morita equivalences of Azumaya algebras on…

We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second…

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties,…

We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two…

We show that Rieffel's deformation sends covariant C(T)-algebras into C(T)-algebras. We also treat the lower semi-continuity issue, proving that Rieffel's deformation transforms covariant continuous fields of C*-algebras into continuous…

As was recently pointed out by McMullen and Taubes [Math. Res. Lett. 6 (1999) 681-696], there are 4-manifolds for which the diffeomorphism group does not act transitively on the deformation classes of orientation-compatible symplectic…

We introduce regular morphisms of topological quivers and show that they give rise to a subcategory of the category of topological quivers and quiver morphisms. Our regularity conditions render the topological quiver C*-algebra construction…

Coisotropic reduction from Poisson geometry and deformation quantization is cast into a general and unifying algebraic framework: we introduce the notion of coisotropic triples of algebras for which a reduction can be defined. This allows…

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic…

Let $A$ and $B$ be two Morita equivalent finite dimensional associative algebras over a field $\Bbbk$. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with…