Related papers: Quadri-algebras
We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism \alpha, which depends not only on the pair (A,\alpha) but also on the choice of a transfer operator (defined in the paper). With this we generalize some…
In this paper, we first explore the extending structures problem by the unified product for anti-dendriform algebras. In particular,the crossed product and non-abelian extension are studied. Furthermore, we explore the inducibility problem…
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…
Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform…
This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to…
Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let $C$ be a binary linear code of length…
A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…
Given an algebra $A$ and an $A-A$-bimodule $U$ with co-algebra structure, a bocs, the algebras of endomorphisms of $A$ as left or right module of the bocs are known as Burt-Butler algebras (up to an appropriate opposite). Here we give a…
We study Rota--Baxter operators on vertex algebras using the integrated $\lambda$-bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the difference between the deformed and original brackets yields…
Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
We introduce the notion of reflexivity for combinatory algebras. Reflexivity can be thought of as an equational counterpart of the Meyer-Scott axiom of combinatory models, which indeed allows us to characterise an equationally definable…
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding…
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field,…
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
The aim of this paper is first to introduce and study Rota-Baxter cosystems and bisystems as generalization of Rota-Baxter coalgebras and bialgebras, respectively, with various examples. The second purpose is to provide an alternative…
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
We introduce a class of permutation centralizer algebras which underly the combinatorics of multi-matrix gauge invariant observables. One family of such non-commutative algebras is parametrised by two integers. Its Wedderburn-Artin…
A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…