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As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
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…
We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of…
This paper studies analogical proportions in monounary algebras consisting only of a universe and a single unary function. We show that the analogical proportion relation is characterized in the infinite monounary algebra formed by the…
We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also…
In this text we are going to discuss the relation between monodromy and algebraic cycles.
In the variety of all linear algebras over the infinite field the difference between geometric and automorphic equivalence of algebras can be big.
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
We study the combinatorics of an analogue of Green's $\mathcal{J}$-relation (a.k.a. the two-sided relation) for the bicategory of finite-dimensional bimodules over finite-dimensional associative algebras over a fixed field. In particular,…
In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…
In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which…
Based on the properties of the poset of those equivalence relations of a multialgebra for which the factor multialgebra is a universal algebra, we give a characterization for the fundamental relations of a multialgebra. We point out the…
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…
This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…
A functional Menger $\cap$-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's compositions of n-place functions and the set-theoretic intersection of functions. We give the abstract…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
If the bimodule of 1-forms of a differential calculus over an associative algebra is the direct sum of 1-dimensional bimodules, a relation with automorphisms of the algebra shows up. This happens for some familiar quantum space calculi.
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…