Related papers: Universal differential calculus on ternary algebra…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
In this article, we describe the construction of graded $q$-differential algebra with ternary differential satisfying the property $d^3=0$ and the $q$-Leibniz rule. Our starting point is coordinate first order differential calculus on some…
In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are…
In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra…
Enveloping $C^*$-algebras for some finitely generated $*$-algebras are considered. It is shown that all of the considered algebras are identically defined by their dual spaces. The description in terms of matrix-functions is given. Keywords…
We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a…
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of…
This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.
This short paper presents a generalisation of Tressl's structure theorem for differentially finitely generated algebras over differential rings of characteristic 0 to the case of separable algebras over differential rings of arbitrary…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…