Related papers: Splitting of Tensor Products and Intermediate Fact…

We prove that the system of Gromov-Witten invariants of the product of two varieties is equal to the tensor product of the systems of Gromov-Witten invariants of the two factors.

We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

We provide a new large class of countable icc groups $\mathcal A$ for which the product rigidity result from [CdSS15] holds: if $\Gamma_1,\dots,\Gamma_n\in\mathcal A$ and $\Lambda$ is any group such that…

We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras…

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning actions of locally compact quantum groups on C*-algebras [S. Baaj, G. Skandalis and S. Vaes, 2003]. Let $\cal G$ be…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

We prove cocontinuity of the $\max$-tensor product of C*-categories and develop a framework to perform factorization homology in a C*-setting. In such context, we specialize some results of D. Ben-Zvi, A. Brochier and D. Jordan. As a…

We study tensor structures on (Rep G)-module categories defined by actions of a compact quantum group G on unital C*-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of…

For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to…

In this article, we consider a twisted partial action $\alpha$ of a group $G$ on a ring $R$ and it is associated partial crossed product $R*_{\alpha}^wG$. We study necessary and sufficient conditions for the commutativity and simplicity of…

It is a classical theorem that the free product of ordered groups is orderable. In this note we show that, using a method of G. Bergman, an ordering of the free product can be constructed in a functorial manner, in the category of ordered…

We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations…

Let $R$ be a principal ideal local ring of finite length with a finite residue field of odd characteristic. Let $G(R)$ denote either the general linear group or the general unitary group of degree two over $R$. We study the decomposition of…

We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a…

We establish the MF property of the reduced group $ C^* $-algebra of an amalgamated free product of countable Abelian discrete groups. This result is then used to give a characterization of the amalgamated free products of Abelian groups…

The groupoid normalisers of a unital inclusion $B\subseteq M$ of von Neumann algebras consist of the set $\mathcal{GN}_M(B)$ of partial isometries $v\in M$ with $vBv^*\subseteq B$ and $v^*Bv\subseteq B$. Given two unital inclusions…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…