相关论文: Bialgebraic Structures and Smarandache Bialgebraic…

We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. By determining when two biquandle structures yield isomorphic biquandles, we obtain a…

All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…

A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak{J}$.

In this paper we construct a bicategory of (super) algebra bundles over a smooth manifold, where the 1-morphisms are bundles of bimodules. The main point is that naive definitions of bimodule bundles will not lead to a well-defined…

There are various generalizations of bialgebras to their ''many object'' versions, such as quantum categories, bialgebroids and weak bialgebras. These can also be thought of as quantum analogues of small categories. In this paper we study…

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class…

All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

An algebraic extended bilinear Hilbert semispace is proposed as being the natural representation space for the algebras of von Neumann.This bilinear Hilbert semispace has a well defined structure given by the representation space of an…

We describe the set of maximal orders in a 2-by-2 matrix algebra over a non-commutative local division algebra B containing a given suborder, for certain important families of such suborders, including rings of integers of division…

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…

An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…

We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset construction known in the theory of n-valued groups. We also consider…

We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…

The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…

The notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras and Hom-Leibniz bialgebras are equivalent in a certain sense. The notion of Hom-Leibniz…