Related papers: The Boardman-Vogt tensor product of operadic bimod…

We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetric monoidal as a bicategory.

We study a mixed tensor product $\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\ell(2|1)$, whenever $q$ is not a root of unity. Formulas…

We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name…

We provide that any Jordan derivation from the block upper triangular matrix algebra $\T = \T(n_{1},n_{2}, \cdots, n_{k})\subseteq M_{n}(\mathbb{\C})$ into a $2$-torsion free unital $\T$-bimodule is the sum of a derivation and an…

We realize the Temperley-Lieb algebra by analogues of Soergel bimodules. The key point is that the monoidal structure is not given by a usual tensor product but by a slightly more complicated operation.

Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category $\mathcal{C}_H$. As a first application, we describe the induced exchange relation for tilting…

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the…

We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbolic motion group of the plane.

The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…

A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with…

A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…

Given two Frobenius algebras, we describe the BV operator on the Hochschild cohomology of their tensor product twisted by a bicharacter in terms of twisted BV operators on summands of the Hochschild cohomology described by Briggs and…

We describe some planar operads build from the higher Bruhat orders.

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…

We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…

The spaces of configurations of non-$k$-overlapping discs have been studied as a bimodule over the little discs operad. In fact, the spaces form a filtered operad. We define and study the induced structure on the homology.

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…