Related papers: Way-below Relation and Tensor Products
For finitely generated modules M and N over a complete intersection R, the vanishing of Tor_i^R(M,N) for all i> 0 gives a tight relationship among depth properties of M, N and their tensor product. Here we concentrate on the converse and…
As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…
A concept of multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows to obtain some concrete results. In particular, the well-known theorem of R. O'Neil about the boundedness…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.
We study representation stability in the sense of Church and Farb. We show that products of stabilizing Sn -representations fulfill certain recursive relations which can be described by a new class of difference operators.
A representational approach to constructing the Fremlin tensor product of two Archimedean Riesz spaces. [Warning: do not view the HTML version!]
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
Given a vector-space $~V~$ which is the tensor product of vector-spaces $A$ and $B$, we reconstruct $A$ and $B$ from the family of simple tensors $a{\otimes}b$ within $V$. In an application to quantum mechanics, one would be reconstructing…
We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
We obtain a faithful representation of the twisted tensor product $B\otimes_{\chi} A$ of unital associative algebras, when $B$ is finite dimensional. This generalizes the representations of [C] where $B=K[X]/<X^2-X>$, [GGV] where…
We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or…
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the…
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a…
Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…