Related papers: Dualities for finite abelian groups and applicatio…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…

In this paper, we will study some connections between Hilbert al- gebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using…

This is a survey on selected developments in the theory of natural dualities where the author had the opportunity to make with his foreign colleagues several breakthroughs and move the theory forward. It is aimed as author's reflection on…

In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

Homomorphism duality pairs play crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be…

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the…

Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…

We start by describing two of the main proposals for duality in Abelian gauge theories, namely $F$(ield strength)-duality approach and the $S$% -duality formalism. We then discuss how $F$-duality and $S$-duality can be applied to the case…

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…

Discrete quantum groups were introduced as duals of compact quantum groups by Podle\'s and Woronowicz in 1990. Shortly after, they were defined and studied intrinsically by Effros and Ruan, and by this author. In 1998, with the introduction…

This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…

Translation association schemes are constructed from actions of finite groups on finite abelian groups satisfying certain natural conditions. It is also shown that the mere existence of maps from finite groups to themselves sending each…

In this article, we study Dorroh extensions of algebras and Dorroh extensions of coalgebras. Their structures are described. Some properties of these extensions are presented. We also introduce the finite duals of algebras and modules which…

Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…

We present some basic theory on the duality of codes over two non-unital rings of order $6$, namely $H_{23}$ and $H_{32}$. For a code $\mathcal{C}$ over these rings, we associate a binary code $\mathcal{C}_a$ and a ternary code…