Related papers: Some classes of topological quasi *-algebras

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone…

We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\A$ defined by locally…

We introduce the nuclear dimension of a C*-algebra; this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank. Our notion behaves well with respect to inductive…

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^*$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of…

If H is a quasi-Hopf algebra and B is a right H-comodule algebra such that there exists v:H\to B a morphism of right H-comodule algebras, we prove that there exists a left H-module algebra A such that B\simeq A# H. The main difference…

Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely required to be continuous. The main examples are groups of $H^s$…

We use braided groups to introduce a theory of $*$-structures on general inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf algebras. This allows the construction of the tensor product of unitary representations up to…

We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld…

Let G be a finite group with cyclic Sylow p-subgroup, and let k be a field of characteristic p. Then H^*(BG;k) and H_*(\Omega BG\phat;k) are A_{\infty} algebras whose structure we determine up to quasi-isomorphism.

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

The mid-seventies' works on C*-algebras of Brown-Douglas-Fillmore and Elliott both contained uniqueness and existence results in a now standard sense. These papers served as keystones for two separate theories -- KK-theory and the…

Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-hereditary algebras admitting a triangular (or…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a semifinite von Neumann algebra isomorphic to the left von Neumann algebra of the Hilbert algebra, as expected. However, in the…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their completions, the number of different rulings, the number of…

We introduce the decomposition rank, a notion of covering dimension for nuclear C^*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to…

The aim of this article is to describe a class of *-algebras that allows to treat well-behaved algebras of unbounded operators independently of a representation. To this end, Archimedean ordered *-algebras (*-algebras whose real linear…

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…

A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple…