Related papers: Notes on divisible MV-algebras
We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\overline{\mathbb{Z}}$- or $\overline{\mathbb{R}}$-categories) and that…
We introduce an endofunctor $H$ on the category $bal$ of bounded archimedean $\ell$-algebras and show that there is a dual adjunction between the category $Alg(H)$ of algebras for $H$ and the category $Coalg(V)$ of coalgebras for the…
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple…
In this paper we show that every locally finite quasivariety of MV-algebras is finitely generated and finitely based. To see this result we study critical MV-algebras. We also give axiomatizations of some of these quasivarieties.
This paper is a sequel to arXiv:2307.13358 and arXiv:2308.16090. A construction associating a semialgebra with an algebra, subalgebra, and a coalgebra dual to the subalgebra played a central role in the author's book arXiv:0708.3398. In…
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 $\Lambda$ be the set of partitions of length $\geq 0$. We introduce an $\mathbb{N}$-graded algebra $\mathbb{A}_q^d(\Lambda)$ associated to $\Lambda$, which can be viewed as a quantization of the algebra of partitions defined by Reineke.…
In this paper, we study a class of $\Z_d$-graded modules, which are constructed using Larsson's functor from $\sl_d$-modules $V$, for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the…
In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…
Pseudo $MV$-algebras are a non-commutative generalization of $MV$-algebras. The main purpose of the paper is to introduce and investigate orthocomplete pseudo $MV$-algebras. We use the concepts of projectable pseudo $MV$-algebras and large…
In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…
We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra $A$ with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk_2(\mp(A))$ of $\mk^b(\mp(A))$ in term of constructible…
Following [Botur, M., Chajda, I., Hala\v{s}, R.: Are basic algebras residuated structures?, Soft Comput. 14 (2010), 251-255] we discuss the connections between left-residuated partially ordered groupoids and the so-called basic algebras,…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We investigate the geometric theory of local MV-algebras and its quotients axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We show that, whilst the theory of local MV-algebras is not of presheaf type, each of…
Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…