Related papers: Additive units of product system

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…

The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The terms in this series are indexed by rooted trees and depend…

The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in…

We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…

Stationary Gaussian generalized random processes having slowly decreasing spectral densities give rise to product systems in the sense of William Arveson (basically, continuous tensor product systems of Hilbert spaces). A continuum of…

This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…

Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…

Let $\mathbf D$ be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On $\BZ\mathbf D$ we define a product and a coproduct, together with an internal product, that is,…

We describe a conjectural construction (in the spirit of Hilbert's 12th problem) of units in abelian extensions of certain base fields which are neither totally real nor CM. These base fields are quadratic extensions with exactly one…

We show that any bijection between two root systems that preserves angles (but not necessarily lengths) gives rise to inequalities relating tensor product multiplicities for the corresponding complex semisimple Lie groups (or Lie algebras).…

Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n>0. We show that there is a numbering {a_i}_{i=1}^n of the elements of A, a numbering {b_i}_{i=1}^n of the…

For the complex Clifford algebra Cl(p,q) of dimension n=p+q we define a Hermitian scalar product. This scalar product depends on the signature (p,q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of…

The notion of left (resp. right) regular object of a tensor C*-category equipped with a faithful tensor functor into the category of Hilbert spaces is introduced. If such a category has a left (resp. right) regular object, it can be…

There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of…

In [On $IP^{\star}$sets and central sets, Combinatorica, 14 (1994) 269-277], N. Hindman and V.Bergelson proved additive $IP^{\star}$-sets contain finite sums and finite products of a single sequence. An analogous study was made by A. Sisto…

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of protomodular, unital and subtractive varieties as well…

We solve two problems in the theory of correspondences that have important implications in the theory of product systems. The first problem is the question whether every correspondence is the correspondence associated (by the representation…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out that they have a very different combinatorial behavior. We…

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to…