Related papers: Constructive Gelfand duality for C*-algebras

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital…

For every finite dimensional Lie supergroup $(G,\mathfrak g)$, we define a $C^*$-algebra $\mathcal A:=\mathcal A(G,\mathfrak g)$, and show that there exists a canonical bijective correspondence between unitary representations of…

We construct in this note a unital properly infinite C*-algebra which is not K$_1$-injective.

We realize Kellendonk'?s C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the tiling, thus providing further evidence that the tight C*-algebra is a good candidate to be the natural…

We give an alternative construction of the essential $C^*$-algebra of an \'etale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity of this essential $C^*$-algebra. In order to do this we…

We introduce a notion of quadratic duality for chiral algebras. This can be viewed as a chiral version of the usual quadratic duality for quadratic associative algebras. We study the relationship between this duality notion and the…

We show that the graph construction used to prove that a gauge-invariant ideal of a graph C*-algebra is isomorphic to a graph C*-algebra, and also used to prove that a graded ideal of a Leavitt path algebra is isomorphic to a Leavitt path…

We construct the weak nonstandard hull of a normed linear space X from *X (the nonstandard extension of X) using the weak topology on X. The bidual (i.e. the second dual) X" is shown to be isometrically isomorphic to the weak nonstandard…

We characterize the topology of the Glimm space of a separable C*-algebra and extend the main result of [6] to non-unital AF C*-algebras.

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 introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…

Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

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…

We construct a simple C*-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang-Su algebra Z, and a hyperfinite II_1 factor not isomorphic to its tensor product with the separable hyperfinite II_1…

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

Let $C$ be a differential graded coalgebra, $ \bar\Omega C$ the Adams cobar construction and $C^\vee$ the dual algebra. We prove that for a large class of coalgebras $C$ there is a natural isomorphism of Gerstenhaber algebras between the…

The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.

We consider a class of partial action groupoids called double groupoids which are constructed from pairs of subgroups satisfying similar conditions to those of a matched pair of groups. If the double groupoid is \'etale, then we show that…