Related papers: Characterizing amalgmation bases for relation, cyl…
We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
For a given extension $A \subset E$ of associative algebras we describe and classify up to an isomorphism all $A$-complements of $E$, i.e. all subalgebras $X$ of $E$ such that $E = A + X$ and $A \cap X = \{0\}$. Let $X$ be a given…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not be true. A finite algebraic structure $\mathbf{A}$ is called…
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We…
We define a class of algebras describing links of binary semi-isolating formulas on a set of realizations for a family of 1-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a…
For a large class of finite W algebras, the defining relations of a Yangian are proved to be satisfied. Therefore such finite W algebras appear as realisations of Yangians. This result is useful to determine properties of such W algebra…
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
Building over recent results, we expand the basic theory of algebraic extensions to the realm of superfields -a field with multivalued sum and product-, showing that every superfield has a (unique up to isomorphism) strong algebraic…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…