Related papers: On a Generalized $*$-Product for Copulas

We provide a reference for basic categorial properties of the categories of (possibly non-unital) $\mathbb{C}$-linear $*$-categories or $C^{*}$-categories, and (not necessarily unit-preserving) functors. Generalizing the classical case of…

The product systems over left cancellative small categories are introduced and studied in this paper. We also introduce the notion of compactly aligned product systems over finite aligned left cancellative small categories and its Nica…

A coproduct on a vector space $A$ is defined as a linear map $\Delta:A\to A\otimes A$ satisfying coassociativity $(\Delta\otimes\iota)\Delta=(\iota\otimes\Delta)\Delta$. We use $\iota$ for the identity map. If $G$ is a finite group and if…

In this paper, we realize C*-algebras of generalized Boolean dynamical systems as partial crossed products. Reciprocally, we give some sufficient conditions for a partial crossed product to be isomorphic to a C*-algebra of a generalized…

The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…

We associate a pro-C*-algebra to a pro-C*-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C*-bimodules and the construction of pro-C*-crossed products by strong bounded…

Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral…

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C^*-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial…

Let $\mathcal{C}_a$ denote the class of associative copulas, and let $\overline{\mathcal{C}}_a$ be the closure, in the uniform metric $d_\infty$, of the convex hull of $\mathcal{C}_a$ . It is known that $\mathcal{C}_a \subseteq…

We construct a generalized version for the free product of unital C*-algebras over a family of unital C*-subalgebras, starting from the group-analogue. When all the subalgebras are the same, we recover the free product with amalgamation…

Recently the author has introduced cobordism-like modules induced from generic maps whose codimensions are negative. They are generalizations of cobordism modules of manifolds. They have been introduced in generalizing the following theorem…

We show that when a co-involutive Hopf C*-algebra $S$ coacts via $\delta$ on a C*-algebra $A$, there exists a full crossed product $A\times_\delta S$, with universal properties analogous to those of full crossed products by locally compact…

Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…

We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for…

Enveloping $C^*$-algebras for some finitely generated $*$-algebras are considered. It is shown that all of the considered algebras are identically defined by their dual spaces. The description in terms of matrix-functions is given. Keywords…

We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C*-algebras agrees…

This paper explores the cup and cap products within the cohomology and homology groups of ample groupoids, focusing on their applications and fundamental properties. Ample groupoids, which are \'etale groupoids with a totally disconnected…

In this paper, we consider the normalized Bessel function of index $\alpha > -\frac{1}{2}$, we find an integral representation of the term $x^nj_{\alpha+n}(x)j_\alpha(y)$. This allows us to establish a product formula for the generalized…

We discuss the crossed product by the dual action of the circle on the crossed product of a C*-algebra A by a Hilbert C*-bimodule X. When X is an A-A Morita equivalence bimodule, the double crossed product is shown to be Morita equivalent…

We introduce polyhedral products in an $\infty$-categorical setting. We generalize a splitting result by Bahri, Bendersky, Cohen, and Gitler that determines the stable homotopy type of the a polyhedral product. We also introduce a motivic…