相关论文: Tensor products of function systems revisited
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are simulated on the algebraic level. This is one of a series of papers on idempotent functional analysis.
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
Let $\mathbf{U}$ be a quantum group of symmetric type. We introduce the {\it thickening realization} to realize (a suitable approximation of) the tensor product ${^{\omega}\Lambda_{\lambda_1}}\otimes \Lambda_{\lambda_2}$ of a simple…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are…
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
The study of matroid products traces back to the 1970s, when Lov\'asz and Mason studied the existence of various types of matroid products with different strengths. Among these, the tensor product is arguably the most important, which can…
In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…
The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.
We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference…
In this paper we prove a series of matching theorems for two sets of Coxeter generators of a finitely generated Coxeter group that identify common features of the two sets of generators. As an application, we describe an algorithm for…
With the aid of utilising tensor products, we give a simplified proof to the fundamental theorem of Benedetto and Fickus about the existence and characterisation of finite, normalised tight frames. We also establish unit-norm tensor…
We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities,…
We introduce the cone of completely-positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a…
We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…
Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear…
Tootkaboni and Vahed introduced the notion of some large sets near idempotent along with some combinatorial properties. We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover,…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…