Related papers: Tensor product decompositions and rigidity of full…

We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of…

In the first part of the paper we survey several results from Popa's deformation/rigidity theory on the classification of tensor product decompositions of large natural classes of II$_1$ factors. Using a m\'elange of techniques from…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…

We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime…

We use malleable deformations combined with spectral gap rigidity theory, in the framework of Popa's deformation/rigidity theory to prove unique tensor product decomposition results for II$_1$ factors arising as tensor product of wreath…

We prove that any tensor product factorization with a commutative factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis. This extends previous work by Carlson and Kov\'acs for the…

In this article, we investigate a unique prime factorization property for infinite tensor product factors. We provide several examples of type II and III factors which satisfy this property, including all free product factors with diffuse…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

We study II_1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result: every finite index M-N-bimodule (in…

In this paper we introduce a new family of icc groups $\Gamma$ which satisfy the following product rigidity phenomenon, discovered in [DHI16] (see also [dSP17]): all tensor product decompositions of the II$_1$ factor $L(\Gamma)$ arise only…

We prove rigidity properties for von Neumann algebraic graph products. We introduce the notion of rigid graphs and define a class of II$_1$-factors named $\mathcal{C}_{\rm Rigid}$. For von Neumann algebras in this class we show a unique…

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

We show that the tensor product $M \mathbin{\overline{\otimes}} N$ of any two full factors $M$ and $N$ (possibly of type ${\rm III}$) is full and we compute Connes' invariant $\tau(M \mathbin{\overline{\otimes}} N)$ in terms of $\tau(M)$…

In this article we investigate the primeness of generalized wreath product II$_1$ factors using deformation/rigidity theory techniques. We give general conditions relating tensor decompositions of generalized wreath products to stabilizers…

Let $I$ be any nonempty set and $(M_i, \varphi_i)_{i \in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $\mathcal C_{\rm anti-free}$ of (possibly type III) von Neumann…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify…

We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader-Shalom and Nevo-Zimmer, we show that the action stabilizers, and all irreducible…

Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee…