Related papers: On monogenic functions defined in different commut…
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
A double algebra is a linear space $V$ equipped with linear map $V\otimes V\to V\otimes V$. Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the…
A commutative algebra over a field gives rise to a representation of the category of finite sets and surjective maps. We consider the restriction of this representation to the subcategory of sets of cardinality at most $r$. For each $r$, we…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
Adjoint functors between the categories of crossed modules of dialgebras and Leibniz algebras are constructed. The well-known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
We define the completion of an associative algebra $A$ in a set $M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the (right) module…