Related papers: Hemi-Nelson algebras
The purpose of this paper is to study Sabinin algebras of Hom-type. It is shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally Sabinin algebras of Hom-type. To this end, we provide a general key construction that…
We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial…
In this paper, we focus on the variety DHMSH of dually hemimorphic semi-Heyting algebras from a logical point of view. Firstly, we present a Hilbert-style axiomatization of a new logic called Dually hemimorphic semi-Heyting logic (DHMSH,…
We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.
A $\nabla$-algebra is a natural generalization of a Heyting algebra, unifying several algebraic structures, including bounded lattices, Heyting algebras, temporal Heyting algebras, and the algebraic representation of dynamic topological…
This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie…
Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas later showed that for finite dimensional algebras of…
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…
The paper is essentially a continuation of B.Plotkin, G.Zhitomirski, "Some logical invariants of algebras and logical relations between algebras", St.Peterburg Math. J., {19:5}, (2008) 859 -- 879, whose main notion is that of…
Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributive lattices with implication and we prove that these are…
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was established. This "new" homological algebra, of derived…
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…
Let A be an abelian category of finite type and homological dimension 1. Then by results of Green R(A), the extended Hall-Ringel algebra of A, has a natural Hopf algebra structure. We consider its Heisenberg double Heis(A) and study its…
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…
The theory of Nichols algebras of diagonal type is known to be closely related to that of semisimple Lie algebras. In this paper the connection between both theories is made closer. For any Nichols algebra of diagonal type invertible…
Happel and Unger reconstructed hereditary algebras from their posets of tilting modules. Inspired by this result, we try removing the assumption to be hereditary. However, it would be unfortunately fail in general: e.g. every selfinjective…
This paper investigates the geometric and algebraic interplay between F-manifolds and a newly defined class of structures termed F$_\text{man}$-algebras. We specialize our study to the category of F-Lie groups, characterized by a Lie group…
This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on…
In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with…
Let $W$ be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras $H_{\bf q}(W)$ as (left) coideal subalgebras. Our Hecke-Hopf algebras ${\bf H}(W)$ have a number of applications. In particular…