相关论文: Wajsberg algebras arising from binary block codes
A code algebra $A_C$ is a nonassociative commutative algebra defined via a binary linear code $C$. In a previous paper, we classified when code algebras are $\mathbb{Z}_2$-graded axial (decomposition) algebras generated by small…
We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and $\text{Heisenberg}\oplus\mathfrak{witt}$ algebras which arise as symmetry algebras in three-dimensional gravity…
The notion of a KU-valued function on a set is introduced and related properties are investigated. Codes generated by KU-valued functions are established. Moreover, we will provide an algorithm which allows us to find a KU-algebra starting…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for…
In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…
The Wyner-Ahlswede-K\"orner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques,…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
We associate quantum vertex algebras and their $\phi$-coordinated quasi modules to certain deformed Heisenberg algebras.
The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a quantum B-algebra with pseudo-product. As an application, we introduce and…
This is the second paper in our series of papers dedicated to the study of maps on the mirror Heisenberg-Virasoro algebra. The first paper is dedicated to the study of unary maps and the present paper is dedicated to the study of binary…
We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated to triangulated surfaces with arbitrarily oriented…
A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined,…
A Hom-Lie-Yamaguti algebra, whose ternary operation expresses through its binary one in a specific way, is a multiplicative Hom-Malcev algebra. Any multiplicative Hom-Malcev algebra over a field of characteristic zero has a natural…
Bicommutative algebras are nonassociative algebras satisfying the polynomial identities of right- and left-commutativity (xy)z=(xz)y and x(yz)=y(xz). We study subvarieties of the variety of all bicommutative algebras over a field of…
We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which…
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…
Quasi-MV* algebras were introduced as generalizations of MV*-algebras and quasi-MV algebras. The recent investigation into quasi-MV* algebras shows that they are closely related to quantum computational logic and complex fuzzy logic. In…
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…
In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary base fields is presented, as well as quadratic form theoretic…