Related papers: Splitting of Tensor Products and Intermediate Fact…

In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…

We introduce the category of C*-discrete inclusions of C*-algebras $A\subset B$ with a faithful conditional expectation $E:B\twoheadrightarrow A$. This class includes many examples such as finite Watatani index inclusions, and also abundant…

Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either semifinite (of type II$_1$ or II$_\infty$,…

We prove that there exists essentially one {\it minimal} differential algebra of distributions $\A$, satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilit\'e de la multiplication des…

Groupoids are the oidification of groups, and they are largely used in topology and representation theory. We consider here the category $\mathsf{Gpd}$ of all groupoids with all morphisms, and the category $\mathsf{Gpd}_\Lambda$ of…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

For any pair $M,N$ of von Neumann algebras such that the algebraic tensor product $M\otimes N$ admits more than one $\mathrm{C}^*$-norm, the cardinal of the set of $\mathrm{C}^*$-norms is at least $ {2^{\aleph_0}}$. Moreover there is a…

Given a partial action \alpha of a group G on an associative algebra A we consider the crossed product A x_\alpha G. Using the algebras of multipliers of ideals of A we prove that A x_\alpha G is associative, provided that all ideals of A…

Let $G$ be a unique product group, i.e., for any two finite subsets $A$ and $B$ of $G$ there exists $x\in G$ which can be uniquely expressed as a product of an element of $A$ and an element of $B$. We prove that, if $C$ is a finite subset…

This paper studies the relationship between minimal dynamical systems on the product of the Cantor set ($X$) and torus ($\T^2$) and their corresponding crossed product $C^*$-algebras. For the case when the cocycles are rotations, we studied…

We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary…

Let $V=\oC^n$ and let $T:=T(V)\otimes T(V^*)$ be the mixed tensor algebra over $V$. We characterize those subsets $A$ of $T$ for which there is a subgroup $G$ of the unitary group $\UU(n)$ such that $A=T^G$. They are precisely the…

Let $X$ be a proper CAT($0$) space and $G$ a cocompact group of isometries of $X$ without fixed point at infinity. We prove that if $\partial X$ contains an invariant subset of circumradius $\pi/2$, then $X$ contains a quasi-dense, closed…

We show that every continuous product system of correspondences over a unital C*-algebra occurs as the product system of a strictly continuous E_0-semigroup.

Let $G$, $H$ be groups. We denote by $\eta(G,H)$ a certain extension of the non-abelian tensor product $G \otimes H$ by $G \times H$. We prove that if $G$ and $H$ are groups that act compatibly on each other and such that the set of all…

For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up to isomorphism. It is trivial if and only…

In this note we prove that the set of all uniformly continuous units on a product system over a C* algebra B can be endowed with the structure of left right B - B Hilbert module after identifying similar units by the suitable equivalence…

We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra $\O_{G,\Lambda}$. We prove that $\O_{G,\Lambda}$ can be realized as the Cuntz-Pimsner algebra of…

We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\times H$ has the same property for every separable compact group $G$. Let $c$ be the cardinality of the continuum. Assuming…