Related papers: Alternative twisted tensor products and Cayley alg…
Although the Cayley-Dickson algebras are twisted group algebras, little attention has been paid to the nature of the Cayley-Dickson twist. One reason is that the twist appears to be highly chaotic and there are other interesting things…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
A twist property is developed which imparts certain properties on the twisted group algebra. These include an involution * satisfying (xy)*=y*x* and an inner product satisfying <xy,z> = <x,zy*> and <xy,z>=<y,x*z>. Examples of twisted group…
We study new coalgebra structures on the tensor product of two coalgebras $C$ and $D$ by twisting the tensor product coalgebra via a twist map $\Psi: C \otimes D \rightarrow D \otimes C$. We deal with the general case in which the counit of…
We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…
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…
The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…
We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…
The purpose of this paper is to provide new constructions of Hom-associative algebras using Hom-analogues of certain operators called twistors and pseudotwistors, by deforming a given Hom-associative multiplication into a new…
The associative Cayley-Dickson algebras over the field of real numbers are also Clifford algebras. The alternative but nonassociative real Cayley-Dickson algebras, notably the octonions and split octonions, share with Clifford algebras an…
In a previous paper we proved a result of the type "invariance under twisting" for Brzezinski's crossed products. In this paper we prove a converse of this result, obtaining thus a characterization of what we call equivalent crossed…
Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for…
In this paper we introduce and study a twisted tensor product construction of nonlocal vertex algebras. Among the main results, we establish a universal property and give a characterization of a twisted tensor product. Furthermore, we give…
Given two associative algebras A, C and a linear space V together with some linear maps R_1, R_2, R_3, E satisfying some conditions, we define an associative algebra structure on A\otimes V\otimes C called a two-sided crossed product.…
We endow twisted tensor products with a natural notion of counit and comultiplication, and we provide sufficient and necessary conditions making the twisted tensor product a counital coassociative coalgebra. We then characterize when the…
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the…
Starting from some ideas given by Bales in [Ba; 09], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley-Dickson process. As a consequence of this result, we prove that an…
The purpose of this paper is to identify all of the Cayley-Dickson doubling products. A Cayley-Dickson algebra $\mathbb{A}_{N+1}$ of dimension $2^{N+1}$ consists of all ordered pairs of elements of a Cayley-Dickson algebra $\mathbb{A}_{N}$…