Related papers: Discrete dualities for some algebras from rough se…
We study the relationship between singularity categories and relative singularity categories and discuss constructions of differential graded algebras of relative singularity categories. As consequences, we obtain structural results, which…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
In recent years, many papers have been published showing relationships between rough sets and some lattice theoretical structures. We present here some strong relations between rough sets and three-valued {\L}ukasiewicz algebras.
This is a slightly corrected version of the article published by Functional Analysis and its Applications in 1993. We define the quadratic duality for algebras with nonhomogeneous relations; the duality between the algebra of differential…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
Here we initiate an investigation of the equational classes of m-symmetric algebras endowed with two tense operators. These varieties is a generalization of tense algebras. Our main interest is the duality theory for these classes of…
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
An algebraic description of basic discrete symmetries (space reversal P, time reversal T and their combination PT) is studied. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers…
Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Let $\mathfrak{g}$ be a finite-dimensional real or complex Lie algebra, and let $\mu \in \mathfrak{g}^{*}$. In the first part of the paper, the relation is discussed between the derived algebra of the stabilizer of $\mu$ and the set of…
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is…
We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…