Related papers: BCK-algebras arising from block codes
We consider the core blocks corresponding to the Hecke algebras of type B over a field of arbitrary characteristic. To each core block B, we associate two non-negative integers which determine the indexing of the Specht modules and simple…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.
We propose an algorithm generating planar networks which structure resembles a hierarchical structure of desiccation crack patterns.
This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients of some ideals in both number fields and cyclic algebras with a suitable trace form. We give criteria for unimodularity. This yields integral and…
We define the block neighborhood of a reversible CA, which is related both to its decomposition into a product of block permutations and to quantum computing. We give a purely combinatorial characterization of the block neighborhood, which…
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-splitting if any given brick is either torsion or…
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
Let $\Lambda$ be a hereditary algebra, $B_0=End_\Lambda(T_0)$ be a tilted algebra. We will construct tilting $B_0$-modules from tilting $\Lambda$-modules and use this result to show how tilting quivers of BB-tilted algebras can be obtained…
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…
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a…
The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…
Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…