相关论文: Some Neutrosophic Algebraic Structures and Neutros…
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
The book "N-ary Groups" (in Russian) consists of two Parts. It is intended on the one hand as an initial introduction to the theory of n-ary groups, and on the other hand it contains the published results by the author on this subject. At…
Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters Tj, Ik, Fl) in neutrosophics. We extend the dialectical triad thesis-antithesis-synthesis to…
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.
Motivated by work of Kac and Lusztig, we define a root system and a Weyl groupoid for a large class of semisimple Yetter-Drinfeld modules over an arbitrary Hopf algebra. The obtained combinatorial structure fits perfectly into an existing…
In this paper which is the first of a series of papers on smooth structures, the concepts of C-structures and smooth structures are introduced and studied. The notion of smooth structure on semi-integral domains is given. It is shown that…
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic…
We introduce so-called "classical" algebraic group over a general base scheme, and then place them where they belong in the classification of reductive groups established in SGA3. We cover the non-split cases and we describe on the way…
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated.…
A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role…
A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric…