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It is shown that a recollement of derived categories of algebras induces those of tensor product algebras and opposite algebras respectively, which is applied to clarify the relations between recollements of derived categories of algebras…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
G\"odel's Dialectica has been introduced and developed in the tradition of the so-called functional interpretations. Only recently has it been related with the a priori unrelated notion of differentiation, by taking a program-theoretic…
In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
Under Stone/Priestley duality for distributive lattices, Esakia spaces correspond to Heyting algebras which leads to the well-known dual equivalence between the category of Esakia spaces and morphisms on one side and the category of Heyting…
The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
In this paper, we introduce the notion of a derivation of a Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of…
Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and…
A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner…
We investigate associativity of multiplications on chain complexes over commutative noetherian rings from two perspectives. First, we introduce a natural associator subcomplex and show how its homology can detect associativity. Second, we…
In this paper we introduce the class of weak Heyting Brouwer algebras (WHB-algebras, for short). We extend the well known duality between distributive lattices and Priestley spaces, in order to exhibit a relational Priestley-like duality…
We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss- Solecki, without the common knowledge operator. We dually…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We describe the problem of Sweedler's duals for bialgebras as essentially characterizing the domain of the transpose of the multiplication. This domain is the set of what could be called ``representative linear forms'' which are the…