Related papers: Some connections between BCK algebras and n ary bl…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…
In this paper we study the categories of braided categorical associative algebras and braided crossed modules of associative algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed…
The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $\alpha$-symmetric and…
At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to them. The current talk deals with Yang-Baxter…
In this paper we give the relationship between the connected components of pure generalized Dynkin graphs and Nichols braided Lie algebras.
This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing…
We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…
This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The first chapter is introductory in nature and gives a few essential definitions and…
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…
We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices.Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic…
We show herein that a pattern based on FGLM techniques can be used for computing Gr\"obner bases, or related structures, associated to linear codes. This Gr\"obner bases setting turns out to be strongly related to the combinatorics of the…
This note describes a technique for generating large non-singular matrices with blocks of full rank. Our motivation to construct such matrices arises in the white-box implementation of cryptographic algorithms with S-boxes.
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…
We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.
This paper introduces and studies the Heun-Racah and Heun-Bannai-Ito algebras abstractly and establishes the relation between these new algebraic structures and generalized Heun-type operators derived from the notion of algebraic Heun…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive…